The chess knight has a unique movement, it may move two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of an L). The possible movements of chess knight are shown in this diagaram:
A chess knight can move as indicated in the chess diagram below:

We have a chess knight and a phone pad as shown below, the knight can only stand on a numeric cell (i.e. blue cell).

Given an integer n, return how many distinct phone numbers of length n we can dial.
You are allowed to place the knight on any numeric cell initially and then you should perform n - 1 jumps to dial a number of length n. All jumps should be valid knight jumps.
As the answer may be very large, return the answer modulo 109 + 7.
 
Example 1:
Input: n = 1
Output: 10
Explanation: We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.

Example 2:
Input: n = 2
Output: 20
Explanation: All the valid number we can dial are [04, 06, 16, 18, 27, 29, 34, 38, 40, 43, 49, 60, 61, 67, 72, 76, 81, 83, 92, 94]

Example 3:
Input: n = 3
Output: 46

Example 4:
Input: n = 4
Output: 104

Example 5:
Input: n = 3131
Output: 136006598
Explanation: Please take care of the mod.

 
Constraints:

1 <= n <= 5000

Difficulty: MEDIUM
Tags: Dynamic programming
Skill types: Dynamic programming

Starter code:
class Solution:
    def knightDialer(self, n: int) -> int:
        

Solutions:
class Solution:
	dp = [[1] * 10]

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		jump = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		for i in range(len(self.dp), n):
			new = [0] * 10
			for j in range(10):
				new[j] = sum((self.dp[-1][k] for k in jump[j])) % MOD
			self.dp.append(new)
		return sum(self.dp[n - 1]) % MOD


from functools import lru_cache
mapping = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
mod = 1000000007

@lru_cache(None)
def dfs(n, i):
	if n == 1:
		return 1
	sum_ = 0
	for nei in mapping[i]:
		sum_ = (sum_ + dfs(n - 1, nei)) % mod
	return sum_

class Solution:

	def knightDialer(self, N: int) -> int:
		total = 0
		for i in range(10):
			total = (total + dfs(N, i)) % mod
		return total


import numpy as np

class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		N = n
		if N == 1:
			return 10
		M = np.matrix([[0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0]])
		(res, N) = (1, N - 1)
		while N:
			if N % 2:
				res = res * M % mod
			M = M * M % mod
			N //= 2
		return int(np.sum(res)) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		possibleMoves = [[4, 6], [6, 8], [9, 7], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		upper = 10 ** 9 + 7
		for i in range(n - 1):
			dp2 = [0] * 10
			for j in range(10):
				for adj in possibleMoves[j]:
					dp2[adj] = (dp2[adj] + dp[j]) % upper
			dp = dp2
		return sum(dp) % upper


class Solution:

	def knightDialer(self, N: int) -> int:
		table = [[0 for col in range(10)] for row in range(N + 1)]
		for val in range(10):
			table[1][val] = 1
		for i in range(2, N + 1):
			table[i][0] = table[i - 1][4] + table[i - 1][6]
			table[i][1] = table[i - 1][6] + table[i - 1][8]
			table[i][2] = table[i - 1][7] + table[i - 1][9]
			table[i][3] = table[i - 1][4] + table[i - 1][8]
			table[i][4] = table[i - 1][3] + table[i - 1][9] + table[i - 1][0]
			table[i][5] = 0
			table[i][6] = table[i - 1][7] + table[i - 1][1] + table[i - 1][0]
			table[i][7] = table[i - 1][2] + table[i - 1][6]
			table[i][8] = table[i - 1][1] + table[i - 1][3]
			table[i][9] = table[i - 1][2] + table[i - 1][4]
		return sum(table[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		move = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		curr_dial = [1] * 10
		for _ in range(n - 1):
			next_dial = [0] * 10
			for key in range(10):
				for neighbor in move[key]:
					next_dial[neighbor] = (next_dial[neighbor] + curr_dial[key]) % (10 ** 9 + 7)
			curr_dial = next_dial
		return sum(curr_dial) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		MOD = 10 ** 9 + 7
		for i in range(N - 1):
			next_dp = [0] * 10
			for j in range(10):
				for next_digit in moves[j]:
					next_dp[j] = (next_dp[j] + dp[next_digit]) % MOD
			dp = next_dp
		return sum(dp) % MOD
		mapping = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [[1] * 10 for _ in range(N)]
		dp[0] = [1] * 10
		for i in range(1, N):
			for j in range(10):
				for k in mapping[j]:
					dp[i][j] += dp[i - 1][k]
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		kmod = 10 ** 9 + 7
		dp = [1] * 10
		for k in range(1, n):
			tmp = [0] * 10
			for i in range(10):
				for j in moves[i]:
					tmp[j] = (tmp[j] + dp[i]) % kmod
			dp = tmp
		res = 0
		for i in range(10):
			res = (res + dp[i]) % kmod
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		valid_moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		m = 10 ** 9 + 7
		for _ in range(n - 1):
			new_dp = [0] * 10
			for i in range(10):
				for j in valid_moves[i]:
					new_dp[j] += dp[i] % m
			dp = new_dp
		return sum(dp) % m


class Solution:

	def knightDialer(self, N: int) -> int:
		moves = [(4, 6), (6, 8), (7, 9), (4, 8), (3, 9, 0), (), (1, 7, 0), (2, 6), (1, 3), (2, 4)]
		memo = [1] * 10
		maxV = 10 ** 9 + 7
		for _ in range(N - 1):
			temp = [0] * 10
			for i in range(10):
				for dest in moves[i]:
					temp[i] += memo[dest]
				temp[i] %= 10 ** 9 + 7
			memo = temp
		return sum(memo) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		dp = [0 for _ in range(10)]
		move = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [4, 2]]
		dp = [1 for _ in range(10)]
		for i in range(n - 1):
			dp2 = [0] * 10
			for j in range(10):
				for nei in move[j]:
					dp2[nei] = (dp2[nei] + dp[j]) % MOD
			dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		movements = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		total = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		for _ in range(n - 1):
			curr = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
			for num in range(10):
				for move in movements[num]:
					curr[move] = (curr[move] + total[num]) % (10 ** 9 + 7)
			total = curr
		return sum(total) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		next_dic = {}
		next_dic[1] = [8, 6]
		next_dic[2] = [7, 9]
		next_dic[3] = [4, 8]
		next_dic[4] = [3, 9, 0]
		next_dic[5] = []
		next_dic[6] = [7, 1, 0]
		next_dic[7] = [2, 6]
		next_dic[8] = [3, 1]
		next_dic[9] = [2, 4]
		next_dic[0] = [6, 4]
		dp = [1] * 10
		for i in range(n - 1):
			dp_new = [0] * 10
			for i in range(10):
				for move in next_dic[i]:
					dp_new[move] = (dp_new[move] + dp[i]) % mod
			del dp
			dp = dp_new
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		current_counts = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		for _ in range(n - 1):
			next_counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
			for src_key in range(10):
				for dst_key in neighbors[src_key]:
					next_counts[dst_key] = (next_counts[dst_key] + current_counts[src_key]) % (10 ** 9 + 7)
			current_counts = next_counts
		return sum(current_counts) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		M = 10 ** 9 + 7
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [0, 1, 7], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		out = [1] * 10
		for _ in range(N - 1):
			out1 = [0] * 10
			for j in range(10):
				for k in d[j]:
					out1[k] += out[j] % M
			out = out1
		return sum(out) % M


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		dic = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [4, 2]}
		counts = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		for k in range(n - 1):
			new = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
			for i in range(10):
				for j in dic[i]:
					new[j] = (new[j] + counts[i]) % mod
			counts = new
		return sum(counts) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		prev = [1] * 10
		for dial in range(n - 1):
			nex = [0] * 10
			for curNum in range(10):
				for nexNum in d[curNum]:
					nex[nexNum] = (nex[nexNum] + prev[curNum]) % (10 ** 9 + 7)
			prev = nex[:]
		return sum(prev) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for _ in range(n - 1):
			dp2 = [0] * 10
			for (i, cnt) in enumerate(dp):
				for nxt in moves[i]:
					dp2[nxt] += cnt
			dp = dp2
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for hop in range(n - 1):
			new_dp = [0] * 10
			for (node, cnt) in enumerate(dp):
				for nei in moves[node]:
					new_dp[nei] += cnt
			dp = new_dp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer1(self, N: int) -> int:
		(m, n) = (4, 3)
		M = 10 ** 9 + 7

		def dp(i, j, k):
			if k == 0:
				return 1
			out = 0
			for (x, y) in [(i + 2, j + 1), (i - 2, j + 1), (i + 2, j - 1), (i - 2, j - 1), (i + 1, j + 2), (i + 1, j - 2), (i - 1, j + 2), (i - 1, j - 2)]:
				if 0 <= x < m and 0 <= y < n and (x != 3 or y not in [0, 2]):
					out += dp(x, y, k - 1)
			return out
		out = 0
		for i in range(m):
			for j in range(n):
				if i != m - 1 or j not in [0, 2]:
					out += dp(i, j, N - 1)
		return out

	def knightDialer(self, N: int) -> int:
		M = 10 ** 9 + 7
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [0, 1, 7], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		out = [1] * 10
		for i in range(N - 1):
			out1 = [0] * 10
			for j in range(10):
				for k in d[j]:
					out1[k] += out[j] % M
			out = out1
		return sum(out) % M


class Solution:

	def helper(self, cache, position, num_hops):
		neighbors = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		if (position, num_hops) in cache:
			return cache[position, num_hops]
		if num_hops == 0:
			return 1
		else:
			num_sequences = 0
			for neighbor in neighbors[position]:
				num_sequences += self.helper(cache, neighbor, num_hops - 1)
			cache[position, num_hops] = num_sequences
		return num_sequences

	def knightDialer(self, n: int) -> int:
		neighbors = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		prior_case = [1] * 10
		current_case = [1] * 10
		current_num_hops = 1
		while current_num_hops < n:
			current_case = [0] * 10
			current_num_hops += 1
			for position in range(0, 10):
				for neighbor in neighbors[position]:
					current_case[position] += prior_case[neighbor]
			prior_case = current_case
		return sum(current_case) % (10 ** 9 + 7)


class Solution:
	BASE = 10 ** 9 + 7

	def knightDialer(self, N: int) -> int:
		if N <= 1:
			return 10
		(a, b, c, d) = (2, 4, 2, 1)
		for _ in range(N - 1):
			(a, b, c, d) = (b, 2 * (a + c) % self.BASE, (b + 2 * d) % self.BASE, c)
		return (a + b + c + d) % self.BASE


class Solution:

	def knightDialer(self, N: int) -> int:
		dic = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [1 for i in range(10)]
		for i in range(N - 1):
			new_dp = [0 for j in range(10)]
			for j in range(10):
				for k in dic[j]:
					new_dp[j] += dp[k]
				new_dp[j] %= 10 ** 9 + 7
			dp = new_dp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		total_jumps = [1] * 10
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		for jumps_left in range(n - 1):
			next_jumps = [0] * 10
			for num in range(0, 10):
				for next_num in neighbors[num]:
					next_jumps[next_num] = next_jumps[next_num] + total_jumps[num] % (10 ** 9 + 7)
			total_jumps = next_jumps
		return sum(total_jumps) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1 for _ in range(10)]
		BASE = 10 ** 9 + 7
		data = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(n - 1):
			dp_tmp = []
			for j in range(10):
				sum_tmp = 0
				for k in data[j]:
					sum_tmp += dp[k] % BASE
				dp_tmp.append(sum_tmp % BASE)
			dp = dp_tmp
		return sum(dp) % BASE


class Solution:

	def knightDialer(self, n):
		dmap = [[4, 6], [8, 6], [7, 9], [8, 4], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4], [4, 6]]
		mod_val = 10 ** 9 + 7
		ans = 0
		dp1 = [1] * 10
		dp2 = [0] * 10
		for _ in range(2, n + 1):
			for j in range(0, 10):
				tv = dmap[j]
				for t in tv:
					dp2[j] += dp1[t] % mod_val
			dp1 = dp2[:]
			dp2 = [0] * 10
		ans = sum(dp1) % mod_val
		return ans


class Solution:

	def __init__(self):
		self.paths = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

	def knightDialer(self, n: int) -> int:
		constant = 10 ** 9 + 7
		if n == 0:
			return 0
		prev_cache = [1 for i in range(10)]
		cache = [0 for i in range(10)]
		for i in range(n - 1):
			for j in range(10):
				total_sum = 0
				for adj_num in self.paths[j]:
					total_sum += prev_cache[adj_num]
				cache[j] = total_sum
			(prev_cache, cache) = (cache, prev_cache)
		return sum(prev_cache) % constant


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		d = dict()
		d[0] = {4, 6}
		d[1] = {6, 8}
		d[2] = {7, 9}
		d[3] = {4, 8}
		d[4] = {0, 3, 9}
		d[6] = {0, 1, 7}
		d[7] = {2, 6}
		d[8] = {1, 3}
		d[9] = {2, 4}
		memo = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		memo2 = [0] * 10
		for i in range(2, n + 1):
			for (key, val) in list(d.items()):
				for v in val:
					memo2[key] += memo[v]
			memo = memo2
			memo2 = [0] * 10
		return sum(memo) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		prior_case = [1] * 10
		current_case = [0] * 10
		current_num_hops = 1
		while current_num_hops < n:
			current_case = [0] * 10
			current_num_hops += 1
			for position in range(0, 10):
				for neighbor in neighbors[position]:
					current_case[position] += prior_case[neighbor]
			prior_case = current_case
		return sum(prior_case) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		cur_count = [1] * 10
		for _ in range(n - 1):
			next_count = [0] * 10
			for src_key in range(10):
				for dst_key in moves[src_key]:
					next_count[dst_key] += cur_count[src_key]
			cur_count = next_count
		return sum(cur_count) % 1000000007


class Solution:

	def knightDialer(self, N: int) -> int:
		MOD = 1000000007
		if N == 1:
			return 10
		(a, b, c, d) = (1, 1, 1, 1)
		for _ in range(N - 1):
			(a, b, c, d) = ((c + b) % MOD, (2 * a + d) % MOD, 2 * a % MOD, 2 * b % MOD)
		return (4 * a + 2 * b + 2 * c + d) % MOD


class Solution(object):

	def knightDialer(self, N):
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for hops in range(N - 1):
			dp2 = [0] * 10
			for (node, count) in enumerate(dp):
				for nei in moves[node]:
					dp2[nei] += count
					dp2[nei] %= MOD
			dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		if n == 1:
			return 10
		pad = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: tuple(), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		current = [0] * 10
		prev = [1] * 10
		for _ in range(n - 1):
			current = [0] * 10
			for key in range(10):
				for bro in pad[key]:
					current[key] += prev[bro]
			prev = current
		return sum(current) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		jump = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [6, 2], 8: [1, 3], 9: [4, 2], 0: [6, 4]}
		dp = [1] * 10
		for _ in range(n - 1):
			new_dp = [0] * 10
			for u in range(10):
				for v in jump[u]:
					new_dp[v] += dp[u]
			dp = new_dp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		transition = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		vec = [1 for _ in range(10)]
		for n in range(1, n):
			new_vec = [0 for _ in range(10)]
			for i in range(0, 10):
				for j in transition[i]:
					new_vec[j] = (new_vec[j] + vec[i]) % (1000000000 + 7)
			vec = new_vec
		return sum(vec) % (1000000000 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		move = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2]}
		pre = [1 for _ in range(10)]
		for i in range(n - 1):
			new = [0 for _ in range(10)]
			for j in range(10):
				for k in move[j]:
					new[k] += pre[j] % (10 ** 9 + 7)
			pre = new
		return sum(pre) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for i in range(n - 1):
			new_dp = [0] * 10
			for (c, val) in enumerate(dp):
				for j in moves[c]:
					new_dp[j] += val
					new_dp[j] %= mod
				dp = new_dp
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for hops in range(n - 1):
			dp2 = [0] * 10
			for (node, count) in enumerate(dp):
				for neighbor in moves[node]:
					dp2[neighbor] += count
					dp2[neighbor] %= MOD
			dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		dct = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [1] * 10
		for _ in range(n - 1):
			nxt = [0] * 10
			for i in range(10):
				for j in dct[i]:
					nxt[j] += dp[i]
			dp = nxt
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		if n == 1:
			return 10
		next_square = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [0, 1, 7], [2, 6], [1, 3], [2, 4], [4, 6]]
		values = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1]
		for i in range(1, n):
			next_values = [0] * 10
			for num in range(10):
				for square in next_square[num]:
					next_values[square] += values[num]
					next_values[square] %= MOD
			values = next_values[:]
		return sum(values) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		MOD = 10 ** 9 + 7
		dp = [1] * 10
		for jumps in range(n - 1):
			temp = [0] * 10
			for i in range(10):
				for nei in moves[i]:
					temp[nei] += dp[i]
					temp[nei] %= MOD
			dp = temp
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		states = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mod = int(1000000000.0) + 7
		for i in range(n - 1):
			dp1 = [0] * 10
			for (j, st) in list(states.items()):
				for k in st:
					dp1[k] += dp[j]
					dp1[k] %= mod
			dp = dp1
		return sum(dp) % mod


move_map = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 0, 7}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		old_row = [1 for _ in move_map]
		new_row = [0 for _ in move_map]
		for N in range(2, n + 1):
			new_row = [0 for _ in move_map]
			for key in move_map:
				res = 0
				for new_key in move_map[key]:
					res += old_row[new_key]
				new_row[key] = res
			old_row = new_row
		return sum(new_row) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		nxt = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp0 = [1] * 10
		for _ in range(1, n):
			dp1 = [0] * 10
			for i in range(10):
				for j in nxt[i]:
					dp1[j] += dp0[i]
			dp0[:] = dp1[:]
		return sum(dp0) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dialer_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		level = [1 for i in range(10)]
		for i in range(1, n):
			next_level = [0 for i in range(10)]
			for l in range(10):
				for d in dialer_map[l]:
					next_level[d] += level[l]
			level = next_level
		return sum(level) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		prev = [1] * 10
		fromMap = {1: {8, 6}, 2: {7, 9}, 3: {4, 8}, 4: {0, 3, 9}, 5: {}, 6: {0, 1, 7}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}, 0: {4, 6}}
		for i in range(1, n):
			dp = [0] * 10
			for k in range(10):
				for j in fromMap[k]:
					dp[k] += prev[j]
					dp[k] %= 10 ** 9 + 7
			prev = dp
		return sum(prev) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		prev = [0] * 10
		dp = [1] * 10
		m = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def parents(x):
			return m[x]
		for l in range(1, n + 1):
			for x in range(10):
				for prevX in parents(x):
					dp[x] = (dp[x] + prev[prevX]) % (10 ** 9 + 7)
			(prev, dp) = (dp, [0] * 10)
		return sum(prev) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if not n:
			return 0
		if n == 1:
			return 10
		steps = [1] * 10
		mapping = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		for i in range(2, n + 1):
			newSteps = [0] * 10
			for i in range(10):
				for j in mapping[i]:
					newSteps[i] += steps[j]
					newSteps[i] %= 10 ** 9 + 7
			steps = newSteps
		return sum(steps) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		dc = {(x, 1): 1 for x in range(10)}
		for i in range(1, n):
			dc[0, i + 1] = (dc[4, i] + dc[6, i]) % mod
			dc[1, i + 1] = (dc[6, i] + dc[8, i]) % mod
			dc[2, i + 1] = (dc[7, i] + dc[9, i]) % mod
			dc[3, i + 1] = (dc[4, i] + dc[8, i]) % mod
			dc[4, i + 1] = (dc[0, i] + dc[3, i] + dc[9, i]) % mod
			dc[5, i + 1] = 0
			dc[6, i + 1] = (dc[0, i] + dc[1, i] + dc[7, i]) % mod
			dc[7, i + 1] = (dc[2, i] + dc[6, i]) % mod
			dc[8, i + 1] = (dc[1, i] + dc[3, i]) % mod
			dc[9, i + 1] = (dc[2, i] + dc[4, i]) % mod
		res = 0
		for j in range(10):
			res = (res + dc[j, n]) % mod
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		dirs = {(-2, -1), (-1, -2), (1, -2), (2, -1), (2, 1), (1, 2), (-1, 2), (-2, 1)}
		prohibited = {(0, 3), (2, 3)}
		graph = {}
		result = [0] * (3 * 4)
		for i in range(3 * 4):
			x1 = i % 3
			y1 = i // 3
			graph[i] = []
			if (x1, y1) in prohibited:
				continue
			for j in range(3 * 4):
				x2 = j % 3
				y2 = j // 3
				if (x2 - x1, y2 - y1) in dirs and (x2, y2) not in prohibited:
					graph[i].append(j)
			result[i] = 1
		M = 10 ** 9 + 7
		for i in range(1, n):
			res_next = [0] * (3 * 4)
			for x in range(3 * 4):
				for adj in graph.get(x, []):
					res_next[x] = (res_next[x] + result[adj]) % M
			result = res_next
		return sum(result) % M


class Solution:

	def knightDialer(self, n: int) -> int:
		KMOD = 10 ** 9 + 7
		moves = [[4, 6], [8, 6], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1 for _ in range(10)]
		for k in range(1, n):
			cur = [0 for _ in range(10)]
			for i in range(10):
				for from_key in moves[i]:
					cur[from_key] += dp[i]
			dp = cur
		result = 0
		for i in range(10):
			result += dp[i]
		return result % KMOD


class Solution:

	def knightDialer(self, n: int) -> int:
		lis = [10, 20, 46, 104, 240, 544]
		if n <= 6:
			return lis[n - 1]
		for i in range(7, n + 1):
			lis.append(6 * lis[-2] - 4 * lis[-4])
		return lis[-1] % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		nxt_pos = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1 for _ in range(10)]
		res = 10
		for _ in range(1, n):
			cur_dp = [0 for _ in range(10)]
			for (val, times) in enumerate(dp):
				for nxt in nxt_pos[val]:
					cur_dp[nxt] += times
					cur_dp[nxt] %= mod
			dp = cur_dp
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		numMoves = {}
		for i in range(10):
			numMoves[1, i] = 1
		for i in range(2, n + 1):
			numMoves[i, 1] = numMoves[i - 1, 6] + numMoves[i - 1, 8] % (10 ** 9 + 7)
			numMoves[i, 2] = numMoves[i - 1, 7] + numMoves[i - 1, 9] % (10 ** 9 + 7)
			numMoves[i, 3] = numMoves[i - 1, 4] + numMoves[i - 1, 8] % (10 ** 9 + 7)
			numMoves[i, 4] = numMoves[i - 1, 3] + numMoves[i - 1, 9] + numMoves[i - 1, 0] % (10 ** 9 + 7)
			numMoves[i, 5] = 0
			numMoves[i, 6] = numMoves[i - 1, 1] + numMoves[i - 1, 7] + numMoves[i - 1, 0] % (10 ** 9 + 7)
			numMoves[i, 7] = numMoves[i - 1, 2] + numMoves[i - 1, 6] % (10 ** 9 + 7)
			numMoves[i, 8] = numMoves[i - 1, 1] + numMoves[i - 1, 3] % (10 ** 9 + 7)
			numMoves[i, 9] = numMoves[i - 1, 2] + numMoves[i - 1, 4] % (10 ** 9 + 7)
			numMoves[i, 0] = numMoves[i - 1, 4] + numMoves[i - 1, 6] % (10 ** 9 + 7)
		totalMoves = 0
		for i in range(10):
			totalMoves += numMoves[n, i]
		return totalMoves % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		result = [1] * 10
		hops = 0
		while hops < n - 1:
			nextResult = [0] * 10
			for idx in range(len(result)):
				for step in moves[idx]:
					nextResult[idx] += result[step]
			result = nextResult
			hops += 1
		return sum(result) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		dic = {0: [4, 6], 1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(1, n):
			temp = dp
			dp = [0] * 10
			for j in range(10):
				if j in dic:
					for k in dic[j]:
						dp[k] += temp[j]
						dp[k] %= 10 ** 9 + 7
		return sum(dp) % (10 ** 9 + 7)


class Solution:
	NEIGHBORS = ((4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4))
	cache = {}

	def get_neighbors(self, n: int) -> Tuple[int]:
		return self.NEIGHBORS[n]

	def knightDialer(self, n: int) -> int:
		results = 0
		prior = [1] * 10
		for _ in range(n - 1):
			current = [0] * 10
			for pos in range(10):
				for neighbor in self.get_neighbors(pos):
					current[pos] += prior[neighbor] % 1000000007
			prior = current
		return sum(prior) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		memo = [1] * 10
		for i in range(n - 1):
			memonext = [0] * 10
			for j in range(10):
				for m in moves[j]:
					memonext[m] += memo[j]
			for j in range(10):
				memo[j] = memonext[j]
		return sum(memo) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		moves = {1: {6, 8}, 2: {9, 7}, 3: {8, 4}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}, 0: {4, 6}}
		dp = [1] * 10
		for i in range(2, N + 1):
			newDp = [0] * 10
			for j in range(10):
				for conn in moves[j]:
					newDp[conn] += dp[j] % (10 ** 9 + 7)
			dp = newDp
		print(dp)
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		res = 0
		path = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [1] * 10
		MOD = 10 ** 9 + 7
		for i in range(2, n + 1):
			dp2 = [0] * 10
			for j in range(10):
				for p in path[j]:
					dp2[j] += dp[p]
			dp = dp2
		res = sum(dp)
		return res % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		reachFrom = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [0, 9, 3], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		prevdp = [1 for _ in range(10)]
		curdp = [0 for _ in range(10)]
		for iteration in range(1, n):
			curdp = [0 for _ in range(10)]
			for i in range(10):
				for nbor in reachFrom[i]:
					curdp[i] += prevdp[nbor]
			prevdp = curdp.copy()
		ans = 0
		for i in range(10):
			ans += prevdp[i]
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		steps = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		ret = set()

		def DFS(cur, i):
			if i == N:
				n = 0
				for c in cur:
					n = n * 10 + c
				ret.add(n)
				print(n)
				return
			for n in steps[cur[-1]]:
				DFS(cur + [n], i + 1)
			return
		for k in list(steps.keys()):
			DFS([k], 1)
		return len(ret)

class Solution:

	def knightDialer(self, N: int) -> int:
		steps = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [1 for _ in range(10)]
		for _ in range(N - 1):
			cur = [0 for _ in range(10)]
			for i in range(10):
				for j in steps[i]:
					cur[j] += dp[i]
			dp = cur
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mappings = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		dp = [1] * 10
		for digit in range(2, n + 1):
			dp2 = [0] * 10
			for (startNumber, counter) in enumerate(dp2):
				for x in mappings[startNumber]:
					dp2[startNumber] += dp[x]
					dp2[startNumber]
			dp = dp2
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		pos_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		num_vals = [1 if i != 5 else 0 for i in range(10)]
		mod_val = 10 ** 9 + 7
		if n == 1:
			return 10
		else:
			for num in range(1, n):
				temp = [0 for i in range(10)]
				for (i, count) in enumerate(num_vals):
					for val in pos_map[i]:
						temp[val] += count
				num_vals = temp
		return sum(num_vals) % mod_val


from collections import deque

class Solution:

	def knightDialer(self, n: int) -> int:
		neighborMap = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (3, 1), 9: (2, 4), 0: (4, 6)}

		def neighbors(pos):
			return neighborMap[pos]

		def countSeq():
			prevMoves = [1] * 10
			curMoves = [0] * 10
			curN = 1
			while curN < n:
				curMoves = [0] * 10
				curN += 1
				for pos in range(10):
					for neighbor in neighbors(pos):
						curMoves[pos] += prevMoves[neighbor]
				prevMoves = curMoves
			curMoves = prevMoves
			return sum(curMoves)
		return countSeq() % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		prev_level = {i: 1 for i in range(10)}
		for j in range(1, n):
			curr_level = defaultdict(int)
			for (i, freq) in list(prev_level.items()):
				for child in d[i]:
					curr_level[child] += freq
			prev_level = curr_level
		return sum(prev_level.values()) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		possible_paths = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [1] * 10
		for i in range(n - 1):
			temp = [0] * 10
			for start_num in range(10):
				for target_num in possible_paths[start_num]:
					temp[target_num] += dp[start_num]
			dp = temp
		return sum(dp) % (7 + 10 ** 9)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		graph = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		MOD = 1000000007
		prev = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1]
		for _ in range(n - 1):
			val = [0] * 10
			for i in range(10):
				for x in graph[i]:
					val[x] += prev[i]
			prev = val
		return sum(prev) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 1000000007
		if n == 0:
			return 0
		dict = {}
		dict[1] = [6, 8]
		dict[2] = [7, 9]
		dict[3] = [4, 8]
		dict[4] = [3, 9, 0]
		dict[5] = []
		dict[6] = [1, 7, 0]
		dict[7] = [2, 6]
		dict[8] = [1, 3]
		dict[9] = [2, 4]
		dict[0] = [4, 6]
		dp = [0] * 10
		for i in range(10):
			dp[i] = [0] * (n + 1)
		for i in range(10):
			dp[i][0] = 0
			dp[i][1] = 1
		sum = 0
		for j in range(2, n + 1):
			for i in range(10):
				for k in dict[i]:
					dp[i][j] = (dp[i][j] + dp[k][j - 1]) % mod
		for i in range(0, 10):
			sum = (sum + dp[i][n]) % mod
		return sum % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		dp_old = [1 for _ in range(10)]
		dp_new = [0 for _ in range(10)]
		possible_next_digits = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		for _ in range(n - 1):
			for j in range(10):
				dp_new[j] = 0
				for digit in possible_next_digits[j]:
					dp_new[j] += dp_old[digit]
			for j in range(10):
				dp_old[j] = dp_new[j]
		total = 0
		for num in dp_new:
			total += num
		return total % (10 ** 9 + 7)


class Solution:
	moveMap = {0: [4, 6], 1: [8, 6], 2: [7, 9], 3: [8, 4], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

	def nextMoves(self, n: int):
		return self.moveMap[n]

	def knightDialer(self, n: int) -> int:
		modulo = 1000000007
		if n < 0:
			return 0
		counts = [1] * 10
		moves = len(self.moveMap)
		while n > 1:
			newCounts = [0] * 10
			for i in range(moves):
				for m in self.nextMoves(i):
					newCounts[m] += counts[i]
			counts = newCounts
			n -= 1
		return sum(counts) % modulo


class Solution:

	def knightDialer(self, n: int) -> int:
		num_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		table = [[0 for _ in range(10)] for _ in range(2)]
		for j in range(10):
			table[0][j] = 1
		for i in range(1, n):
			for j in range(10):
				sum_d = 0
				for d in num_map[j]:
					sum_d += table[(i - 1) % 2][d]
				table[i % 2][j] = sum_d
		return sum(table[(n - 1) % 2]) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		from collections import defaultdict
		dct = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = {1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1, 0: 1}
		n -= 1
		while n > 0:
			new_dp = defaultdict(int)
			for num1 in dp:
				for num2 in dct[num1]:
					new_dp[num2] += dp[num1]
			dp = new_dp
			n -= 1
		ans = 0
		for key in dp:
			ans += dp[key]
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		M = 10 ** 9 + 7
		moves = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		prior_n = [1] * 10
		for hops in range(2, n + 1):
			curr_n = [0] * 10
			for (num, count) in enumerate(prior_n):
				for nbr in moves[num]:
					curr_n[nbr] += count
					curr_n[nbr] %= M
			prior_n = curr_n
		return sum(prior_n) % M


class Solution:

	def knightDialer(self, n: int) -> int:
		validJumps = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		memo = [[0 for _ in range(n + 1)] for _ in range(10)]
		for i in range(len(memo)):
			memo[i][1] = 1
		for j in range(2, n + 1):
			for i in range(len(memo)):
				for k in validJumps[i]:
					memo[i][j] = (memo[i][j] + memo[k][j - 1]) % (10 ** 9 + 7)
		ans = 0
		for i in range(10):
			ans = (ans + memo[i][n]) % (10 ** 9 + 7)
		return ans


from functools import lru_cache
mapping = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
mod = 1000000007

@lru_cache(None)
def f(n: int, d: int) -> int:
	if n == 1:
		return 1
	s = 0
	for d1 in mapping[d]:
		s = (s + f(n - 1, d1)) % mod
	return s

class Solution:

	def knightDialer(self, N: int) -> int:
		tot = 0
		for d in range(10):
			tot = (tot + f(N, d)) % mod
		return tot


class Solution:

	def knightDialer(self, n: int) -> int:
		adj_lists = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		table = [[1] * 10 for i in range(n)]
		for n0 in range(1, n):
			for digit in range(10):
				acc = 0
				for adj in adj_lists[digit]:
					acc += table[n0 - 1][adj]
				table[n0][digit] = acc
		return sum(table[n - 1]) % (10 ** 9 + 7)


from collections import defaultdict

class Solution:

	def knightDialer(self, n: int) -> int:
		_nextMove = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		moves = {i: 1 for i in range(10)}
		while n > 1:
			newmoves = defaultdict(int)
			for (k, v) in moves.items():
				for _next in _nextMove[k]:
					newmoves[_next] += v
			moves = newmoves
			n -= 1
		return sum(moves.values()) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		positions = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [[0 for i in range(n + 1)] for i in range(10)]
		for i in range(10):
			dp[i][1] = 1
		for j in range(2, n + 1):
			for i in range(10):
				for pos in positions[i]:
					dp[i][j] = (dp[i][j] + dp[pos][j - 1]) % 1000000007
		result = 0
		for i in range(10):
			result = (result + dp[i][n]) % 1000000007
		return result


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		dic = {0: (4, 6), 1: (8, 6), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		dp = [1] * 10
		for _ in range(n - 1):
			new = [0] * 10
			for i in range(10):
				for nei in dic[i]:
					new[i] += dp[nei]
					new[i] %= 10 ** 9 + 7
			dp = new
		return sum(dp) % (10 ** 9 + 7)


MOD = 10 ** 9 + 7
num_to_next = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		dp = [1 for _ in range(10)]
		for _ in range(n - 1):
			next_dp = [0 for _ in range(10)]
			for current in range(10):
				for next_pos in num_to_next[current]:
					next_dp[next_pos] += dp[current]
					next_dp[next_pos] = next_dp[next_pos] % MOD
			dp = next_dp
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		dp = [1] * 10
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		for hop in range(n - 1):
			dp2 = [0] * 10
			for (i, move) in enumerate(moves):
				count = dp[i]
				for pos in move:
					dp2[pos] += count
					dp2[pos] %= MOD
			dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		numpad = {'0': ['4', '6'], '1': ['6', '8'], '2': ['7', '9'], '3': ['4', '8'], '4': ['0', '3', '9'], '6': ['0', '1', '7'], '7': ['2', '6'], '8': ['1', '3'], '9': ['4', '2']}
		dp = {}
		for i in ['0', '1', '2', '3', '4', '6', '7', '8', '9']:
			dp[i] = []
			dp[i].append(1)
		for i in range(1, n):
			for j in ['0', '1', '2', '3', '4', '6', '7', '8', '9']:
				dp[j].append(0)
				for k in numpad[j]:
					dp[j][i] += dp[k][i - 1]
				dp[j][i] %= 1000000007
		res = 0
		for i in ['0', '1', '2', '3', '4', '6', '7', '8', '9']:
			res += dp[i][n - 1]
			res %= 1000000007
		return res


import collections

class Solution:

	def knightDialer(self, m: int) -> int:
		MOD = 10 ** 9 + 7
		n = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		end = {}
		for ab in range(10):
			end[ab] = 1
		for a in range(1, m):
			end2 = {}
			for ab in range(10):
				end2[ab] = 0
			for key in range(10):
				val = n[key]
				for c in val:
					end2[key] += end[c]
			end = end2
		return sum(end.values()) % MOD


import logging
LOG = logging.getLogger(__name__)
MODULO = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		counts = [2, 2, 3, 2]
		for _ in range(n - 2):
			next_counts = [counts[1] + counts[2], 2 * counts[0], 2 * counts[0] + counts[3], 2 * counts[2]]
			counts = next_counts
		return (4 * counts[0] + 2 * counts[1] + 2 * counts[2] + counts[3]) % MODULO


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		if n == 1:
			return 10
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (8, 4), 4: (3, 9, 0), 5: tuple(), 6: (7, 1, 0), 7: (2, 6), 8: (1, 3), 9: (4, 2)}
		prev_jump = [1] * 10
		curr_jump = [0] * 10
		jump = 0
		for jump in range(0, n - 1):
			curr_jump = [0] * 10
			for num in range(0, 10):
				for i in neighbors[num]:
					curr_jump[i] += prev_jump[num]
					curr_jump[i] %= MOD
			prev_jump = curr_jump
		return sum(curr_jump) % MOD


class Solution:

	def knightDialer(self, N: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for n in range(N - 1):
			newdp = [0] * 10
			for i in range(10):
				for j in moves[i]:
					newdp[i] += dp[j]
					newdp[i] %= 10 ** 9 + 7
			dp = newdp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		d = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [1] * 10
		for i in range(1, n):
			dp_l = [0] * 10
			for (sq, count) in enumerate(dp):
				for neigh in d[sq]:
					dp_l[neigh] += count
					dp_l[neigh] %= 10 ** 9 + 7
			dp = dp_l
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [3, 1], 9: [4, 2]}
		res = 0
		dp = [1] * 10
		for x in range(1, n):
			temp = [0] * 10
			for i in range(10):
				for j in d[i]:
					temp[j] += dp[i]
			dp = temp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[] for x in range(10)]
		moves[0] = [4, 6]
		moves[1] = [6, 8]
		moves[2] = [7, 9]
		moves[3] = [4, 8]
		moves[4] = [3, 9, 0]
		moves[5] = []
		moves[6] = [0, 1, 7]
		moves[7] = [2, 6]
		moves[8] = [1, 3]
		moves[9] = [2, 4]
		dp = {}

		def dialer(start, n):
			if (start, n) in dp:
				return dp[start, n]
			if n == 1:
				dp[start, n] = 1
				return 1
			xmoves = 0
			for move in moves[start]:
				xmoves += dialer(move, n - 1)
			xmoves %= 10 ** 9 + 7
			dp[start, n] = xmoves
			return xmoves
		xmoves = 0
		for i in range(0):
			xmoves += dialer(i, n)
			print(('i ', i, 'moves', dialer(i, n), 'tot ', xmoves))
		prev = [1] * 10
		for hop in range(2, n + 1):
			curr = [0] * 10
			for i in range(10):
				for move in moves[i]:
					curr[i] += prev[move]
			prev = curr
		return sum(prev) % (10 ** 9 + 7)


class Solution:

	def knight(self, n, current, memo):
		knight_mp = {1: {8, 6}, 2: {9, 7}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {7, 1, 0}, 7: {2, 6}, 8: {3, 1}, 9: {2, 4}, 0: {6, 4}}
		if n == 1:
			return 1
		if (current, n) in memo:
			return memo[current, n]
		res = 0
		for item in knight_mp.get(current, set()):
			res += self.knight(n - 1, item, memo)
		memo[current, n] = res
		return res

	def knightDialer(self, n: int) -> int:
		knight_mp = {1: {8, 6}, 2: {9, 7}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {7, 1, 0}, 7: {2, 6}, 8: {3, 1}, 9: {2, 4}, 0: {6, 4}}
		prev = [1 for _ in range(0, 10)]
		mod = 10 ** 9 + 7
		for step in range(1, n):
			curr = [0 for _ in range(0, 10)]
			for cell in range(0, 10):
				for neighbor in knight_mp.get(cell, set()):
					curr[cell] += prev[neighbor]
			prev = curr
		return sum(prev) % mod


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 1:
			return 10
		nums = [1, 1, 1, 1]
		for _ in range(N - 1):
			nums = [nums[1] + nums[2], 2 * nums[0], 2 * nums[0] + nums[3], 2 * nums[2]]
		return (4 * nums[0] + 2 * nums[1] + 2 * nums[2] + nums[3]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		el = [[] for i in range(10)]
		el[0] = [4, 6]
		el[1] = [6, 8]
		el[2] = [7, 9]
		el[3] = [4, 8]
		el[4] = [3, 9, 0]
		el[5] = []
		el[6] = [1, 7, 0]
		el[7] = [2, 6]
		el[8] = [1, 3]
		el[9] = [2, 4]
		a = [[0 for i in range(10)] for j in range(n)]
		for i in range(10):
			a[0][i] = 1
		for i in range(1, n):
			for j in range(10):
				for x in el[j]:
					a[i][j] = (a[i][j] + a[i - 1][x]) % (10 ** 9 + 7)
		c = 0
		for i in range(10):
			c += a[-1][i]
		return c % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		adj = {}
		adj[0] = [4, 6]
		adj[1] = [6, 8]
		adj[2] = [7, 9]
		adj[3] = [4, 8]
		adj[4] = [0, 3, 9]
		adj[5] = []
		adj[6] = [0, 1, 7]
		adj[7] = [2, 6]
		adj[8] = [1, 3]
		adj[9] = [2, 4]
		p = 10 ** 9 + 7
		f = [None] * n
		f[0] = [1] * 10
		for i in range(1, n):
			f[i] = [0] * 10
			for v in range(0, 10):
				for u in adj[v]:
					f[i][v] += f[i - 1][u]
		total = 0
		for d in range(0, 10):
			total = (total % p + f[n - 1][d] % p) % p
		return total


class Solution:

	def knightDialer(self, n: int) -> int:
		possibilities = {2: {9, 7}, 1: {8, 6}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {6, 2}, 8: {1, 3}, 9: {4, 2}, 0: {4, 6}}

		def dp(n):
			result = {i: 1 for i in range(10)}
			for i in range(2, n + 1):
				temp = defaultdict(int)
				for curr_position in result:
					for next_position in possibilities[curr_position]:
						temp[next_position] += result[curr_position]
				result = temp
			return sum(result.values()) % (pow(10, 9) + 7)
		return dp(n)


class Solution:

	def knightDialer(self, n: int) -> int:
		cur_state = [1 for _ in range(10)]
		mod = 10 ** 9 + 7
		edges = [(1, 6), (1, 8), (2, 7), (2, 9), (3, 4), (3, 8), (4, 9), (4, 0), (6, 7), (6, 0)]
		edge_dic = {i: [] for i in range(10)}
		for (i, j) in edges:
			edge_dic[i].append(j)
			edge_dic[j].append(i)
		for _ in range(1, n):
			new_state = [0 for _ in range(10)]
			for i in range(10):
				new_state[i] = sum([cur_state[j] for j in edge_dic[i]]) % mod
			cur_state = new_state
		return sum(cur_state) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		d = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [[1] * 10]
		dp += [[0] * 10 for i in range(n - 1)]
		for i in range(n - 1):
			for j in range(10):
				for k in d[j]:
					dp[i + 1][k] = (dp[i + 1][k] + dp[i][j]) % 1000000007
		return sum(dp[-1]) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for i_n in range(n - 1):
			dp2 = [0] * 10
			for i in range(10):
				for nei in moves[i]:
					dp2[nei] += dp[i]
					dp2[nei] %= MOD
			dp = list(dp2)
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = int(1000000000.0 + 7)
		adj = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [[0] * 10 for _ in range(n + 1)]
		dp[1] = [1] * 10
		for i in range(2, n + 1):
			for j in range(10):
				for child in adj[j]:
					dp[i][j] += dp[i - 1][child]
					dp[i][j] %= MOD
		ans = 0
		for v in dp[n]:
			ans += v
			ans %= MOD
		return ans


from collections import Counter

class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		if n == 1:
			return 10
		starts = dict([(i, 1) for i in moves])
		for _ in range(n - 1):
			next = dict([(i, 0) for i in moves])
			for i in starts:
				for j in moves[i]:
					next[j] += starts[i]
			starts = next
		return sum(starts.values()) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		c = [1, 2, 2, 4]
		nx = [0, 0, 0, 0]
		for i in range(n - 1):
			nx[0] = c[1]
			nx[1] = 2 * c[0] + c[3]
			nx[2] = c[3]
			nx[3] = 2 * (c[1] + c[2])
			c = nx[:]
		return sum(c) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [9, 7], [8, 4], [3, 9, 0], [], [7, 1, 0], [6, 2], [1, 3], [2, 4]]
		count = [[0] * 10 for _ in range(n + 1)]
		for i in range(10):
			count[1][i] = 1
		for i in range(1, n + 1):
			for num in range(10):
				for nei in moves[num]:
					count[i][num] += count[i - 1][nei]
					count[i][num] %= 10 ** 9 + 7
		return sum(count[-1]) % (10 ** 9 + 7)


class Solution:
	neighbors = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		if n == 1:
			return 10
		prev_moves = [1] * 10
		current_moves = [0] * 10
		for i in range(n - 1):
			for j in range(10):
				current_moves[j] = sum((prev_moves[k] for k in self.neighbors[j])) % (10 ** 9 + 7)
			prev_moves = current_moves[:]
		return sum(prev_moves) % (10 ** 9 + 7)


MODULE = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		MOVEMENTS = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [2, 2, 2, 2, 3, 0, 3, 2, 2, 2]
		for idx in range(2, n):
			new_dp = [0] * 10
			for jdx in range(10):
				for next_jdx in MOVEMENTS[jdx]:
					new_dp[next_jdx] += dp[jdx]
			dp = new_dp
		print(dp)
		return sum(dp) % MODULE


class Solution:

	def knightDialer(self, n: int) -> int:
		adj = [[4, 6], [8, 6], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		m = 10 ** 9 + 7
		memo = [1] * 10
		for i in range(1, n):
			memo = [sum((memo[e] for e in adj[d])) % m for d in range(10)]
		return sum(memo) % m


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		moves = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		curr = [1] * 10
		for _ in range(n - 1):
			nex = [0] * 10
			for i in range(10):
				nex[i] = sum((curr[j] for j in moves[i])) % mod
			curr = nex
		return sum(curr) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		res = 0
		mappings = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [[0 for i in range(10)] for i in range(n + 1)]
		dp[0] = [1 for i in range(10)]
		dp[1] = [len(mappings[i]) for i in range(10)]
		for i in range(1, n - 1):
			for j in range(10):
				pos = mappings[j]
				for k in pos:
					dp[i + 1][k] += dp[i][j]
		return sum(dp[n - 1]) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		movedict = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		DP = [[0] * 10 for _ in range(n)]
		DP[0] = [1] * 10
		for l in range(1, n):
			for s in range(10):
				for moveto in movedict[s]:
					DP[l][s] += DP[l - 1][moveto]
					DP[l][s] %= MOD
		ans = sum(DP[-1]) % MOD
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		nextMove = [(4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4)]
		dp = [[0] * 10 for _ in range(n)]
		if n == 1:
			return 10
		MOD = 10 ** 9 + 7
		for i in range(10):
			dp[0][i] = 1
		for r in range(1, n):
			for i in range(10):
				for m in nextMove[i]:
					dp[r][m] = dp[r][m] + dp[r - 1][i]
		return sum(dp[-1]) % MOD


class Solution(object):

	def knightDialer(self, N):
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		MOD = 10 ** 9 + 7
		table = [1] * 10
		for _ in range(N - 1):
			temp = [0] * 10
			for k in range(10):
				temp[k] = sum((table[i] for i in moves[k]))
				temp[k] %= MOD
			table = temp
		return sum(table) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		(a, b, c, d) = [1, 2, 2, 4]
		for i in range(n - 1):
			(a, b, c, d) = [b, 2 * a + d, d, 2 * (b + c)]
		return sum([a, b, c, d]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n):
		max_val = 10 ** 9 + 7
		mem = {(1, 1): 1, (1, 2): 1, (1, 3): 1, (1, 4): 1, (1, 5): 1, (1, 6): 1, (1, 7): 1, (1, 8): 1, (1, 9): 1, (1, 0): 1}
		fields = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (3, 1), 9: (2, 4)}
		new_mem = {}
		for length in range(1, n):
			for num in range(10):
				possible_jumps = fields[num]
				possible_paths = 0
				for jump in possible_jumps:
					possible_paths = (possible_paths + mem[length, jump]) % max_val
				new_mem[length + 1, num] = possible_paths
			mem = new_mem
			new_mem = {}
		result = 0
		for key in list(mem.keys()):
			result = (result + mem[key]) % max_val
		return result % max_val


class Solution:

	def knightDialer(self, N: int) -> int:
		jumps = dict({1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]})
		table = [[0] * N for i in range(10)]
		for j in range(N):
			for i in range(10):
				if j == 0:
					table[i][0] = 1
				elif j == 1:
					table[i][j] = len(jumps[i])
				else:
					kList = jumps[i]
					for k in kList:
						table[i][j] += table[k][j - 1]
		res = 0
		for i in range(len(table)):
			res = (res + table[i][-1]) % (10 ** 9 + 7)
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [[0 for _ in range(n + 1)] for _ in range(10)]
		for i in range(10):
			dp[i][1] = 1
		for j in range(2, n + 1):
			for i in range(10):
				for move in moves[i]:
					dp[i][j] += dp[move][j - 1]
					dp[i][j] %= MOD
		sum_ = 0
		for i in range(10):
			sum_ += dp[i][n]
			sum_ %= MOD
		return sum_


class Solution:

	def knightDialer(self, N: int) -> int:
		steps = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [1 for _ in range(10)]
		for _ in range(N - 1):
			cur = [0 for _ in range(10)]
			for i in range(10):
				for j in steps[i]:
					cur[j] += dp[i]
			dp = cur
		return sum(dp) % (10 ** 9 + 7)


class Solution:
	d = [(4, 6), (6, 8), (7, 9), (4, 8), (3, 9, 0), (), (1, 7, 0), (2, 6), (1, 3), (2, 4)]
	cache = {}

	def dfs(self, i, n):
		if n == 0:
			return 1
		elif (i, n) not in self.cache:
			self.cache[i, n] = sum((self.dfs(val, n - 1) for val in self.d[i]))
			if i in [1, 4, 7]:
				self.cache[i + 2, n] = self.cache[i, n]
			elif i in [3, 6, 9]:
				self.cache[i - 2, n] = self.cache[i, n]
		return self.cache[i, n]

	def knightDialer(self, n: int) -> int:
		return sum((self.dfs(i, n - 1) for i in range(10))) % (int(1000000000.0) + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		mod = 10 ** 9 + 7
		dp = [[0 for i in range(n + 1)] for j in range(10)]
		for i in range(10):
			dp[i][1] = 1
		d = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for j in range(2, n + 1):
			for i in range(10):
				if i != 5:
					for ele in d[i]:
						dp[i][j] += dp[ele][j - 1]
						dp[i][j] %= mod
		ans = 0
		for i in range(10):
			ans += dp[i][n]
			ans %= mod
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[0 for _ in range(10)] for _ in range(n + 1)]
		prevs = {0: [4, 6], 1: [8, 6], 2: [7, 9], 3: [8, 4], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [4, 2]}
		for i in range(10):
			dp[1][i] = 1
		for i in range(2, n + 1):
			for j in range(10):
				for prev in prevs[j]:
					dp[i][j] += dp[i - 1][prev]
		return sum(dp[-1]) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		arr = [[0 for i in range(10)] for i in range(n)]
		mappings = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mod = 10 ** 9 + 7
		arr[0] = [1 for i in range(10)]
		for i in range(1, n):
			for j in range(10):
				for k in mappings[j]:
					arr[i][j] += arr[i - 1][k]
		return sum(arr[n - 1]) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		N = n
		l = 10
		dp = [1] * l
		m = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		for _ in range(2, N + 1):
			dp2 = [0] * l
			for i in range(l):
				for j in m[i]:
					dp2[i] += dp[j]
			dp = dp2
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		next_move = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = defaultdict(int)
		for i in range(10):
			memo[i] = 1
		for _ in range(n - 1):
			next_memo = defaultdict(int)
			for i in range(10):
				for next_step in next_move[i]:
					next_memo[next_step] += memo[i]
					next_memo[next_step] %= 10 ** 9 + 7
			memo = next_memo
		return sum(memo.values()) % (10 ** 9 + 7)


MOVES = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
modulus = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		dp2 = [0] * 10
		for _ in range(1, n):
			for digit in range(10):
				dp2[digit] = 0
				for next_digit in MOVES[digit]:
					dp2[digit] += dp[next_digit]
					dp2[digit] %= modulus
			(dp2, dp) = (dp, dp2)
		result = 0
		for ways in dp:
			result += ways
			result %= modulus
		return result


class Solution:

	def knightDialer(self, n: int) -> int:
		achievable = {}
		achievable[0] = [4, 6]
		achievable[1] = [6, 8]
		achievable[2] = [7, 9]
		achievable[3] = [4, 8]
		achievable[4] = [0, 3, 9]
		achievable[5] = []
		achievable[6] = [0, 1, 7]
		achievable[7] = [2, 6]
		achievable[8] = [1, 3]
		achievable[9] = [2, 4]
		f1 = [1 for _ in range(10)]
		m = 10 ** 9 + 7
		for i in range(1, n):
			f2 = [0 for _ in range(10)]
			for j in range(10):
				f2[j] = sum((f1[l] for l in achievable[j])) % m
			f1 = f2.copy()
		return sum(f1) % m


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mem = [[0 for i in range(n)] for i in range(10)]
		for i in range(10):
			mem[i][0] = 1
		for col in range(1, n):
			for row in range(10):
				for move in moves[row]:
					mem[row][col] += mem[move][col - 1]
					mem[row][col] %= 10 ** 9 + 7
		tot_sum = 0
		for row in range(10):
			tot_sum += mem[row][n - 1]
			tot_sum %= 10 ** 9 + 7
		return tot_sum


class Solution:

	def knightDialer(self, n: int) -> int:
		tab = [[0 for i in range(n + 1)] for i in range(10)]
		for i in range(10):
			tab[i][1] = 1
		for i in range(2, n + 1):
			for j in range(10):
				if j == 0:
					tab[j][i] = tab[4][i - 1] + tab[6][i - 1]
				if j == 1:
					tab[j][i] = tab[6][i - 1] + tab[8][i - 1]
				if j == 2:
					tab[j][i] = tab[7][i - 1] + tab[9][i - 1]
				if j == 3:
					tab[j][i] = tab[4][i - 1] + tab[8][i - 1]
				if j == 4:
					tab[j][i] = tab[3][i - 1] + tab[9][i - 1] + tab[0][i - 1]
				if j == 5:
					tab[j][i] = 0
				if j == 6:
					tab[j][i] = tab[1][i - 1] + tab[7][i - 1] + tab[0][i - 1]
				if j == 7:
					tab[j][i] = tab[2][i - 1] + tab[6][i - 1]
				if j == 8:
					tab[j][i] = tab[1][i - 1] + tab[3][i - 1]
				if j == 9:
					tab[j][i] = tab[2][i - 1] + tab[4][i - 1]
				tab[j][i] = tab[j][i] % (10 ** 9 + 7)
		s = 0
		for i in range(10):
			s += tab[i][n]
		s = s % (10 ** 9 + 7)
		return s


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [4, 2]]
		ct = [1] * 10
		while n - 1:
			ct = [sum((ct[j] for j in i)) for i in dp]
			n -= 1
		return sum(ct) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dic = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (1, 0, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		prev_dic = {}
		for i in range(10):
			prev_dic[i] = 1
		for i in range(n - 1):
			cur_dic = collections.defaultdict(int)
			for j in prev_dic:
				for k in dic[j]:
					cur_dic[k] += prev_dic[j]
			prev_dic = cur_dic
		return sum(prev_dic.values()) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for cell in range(n - 1):
			dp2 = [0] * 10
			for (num_cell, count) in enumerate(dp):
				for knight in moves[num_cell]:
					dp2[knight] += count
					dp2[knight] %= MOD
				dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [[0 for j in range(10)] for i in range(n)]
		for i in range(n):
			for j in range(10):
				if i == 0:
					dp[i][j] = 1
				else:
					for move in moves[j]:
						dp[i][j] += dp[i - 1][move]
		return sum(dp[n - 1]) % (10 ** 9 + 7)


import numpy as np

class Solution:

	def knightDialer(self, n: int) -> int:
		(memo, dp) = ([[4, 6], [8, 6], [7, 9], [4, 8], [3, 9, 0], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]], [1] * 10)
		for i in range(n - 1):
			dp = [sum([dp[j] for j in memo[i]]) for i in range(10)]
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[0 for _ in range(n + 1)] for _ in range(10)]
		next_map = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		MOD = pow(10, 9) + 7
		for i in range(10):
			dp[i][1] = 1
		for k in range(2, n + 1):
			for i in range(10):
				for next_num in next_map[i]:
					dp[i][k] += dp[next_num][k - 1] % MOD
					dp[i][k] %= MOD
		ans = 0
		for i in range(10):
			ans += dp[i][n]
			ans %= MOD
		return ans


class Solution:

	def knightDialer(self, k: int) -> int:
		self.dirs = [[1, 2], [1, -2], [-1, 2], [-1, -2], [2, 1], [2, -1], [-2, 1], [-2, -1]]
		self.mod = 10 ** 9 + 7
		self.n = 4
		self.m = 3
		if k == 1:
			return 10
		self.forbidden = set([(3, 0), (3, 2)])
		self.next_pos = self.build_pos()
		self.dp = [1] * 10
		self.helper(k - 1)
		return sum(self.dp) % self.mod

	def helper(self, k):
		if k == 0:
			return
		next_dp = [0] * 10
		for i in range(10):
			for j in self.next_pos[i]:
				next_dp[j] += self.dp[i] % self.mod
				next_dp[j] %= self.mod
		self.dp = next_dp
		self.helper(k - 1)

	def build_pos(self):
		res = {}
		for i in range(10):
			next_num = []
			(x, y) = self.get_pos(i)
			for d in self.dirs:
				(nx, ny) = d
				if self.is_valid(x + nx, y + ny):
					num = self.get_num(x + nx, y + ny)
					next_num.append(num)
			res[i] = next_num
		return res

	def is_valid(self, x, y):
		return 0 <= x < self.n and 0 <= y < self.m and ((x, y) not in self.forbidden)

	def get_num(self, x, y):
		if x == 3 and y == 1:
			return 0
		if self.is_valid(x, y):
			return x * 3 + y + 1

	def get_pos(self, num):
		if num == 0:
			return (3, 1)
		num -= 1
		row = num // 3
		col = num % 3
		return (row, col)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		m = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		cnt = defaultdict(int)
		for k in m:
			for v in m[k]:
				cnt[v] += 1
		for _ in range(n - 2):
			cnt2 = defaultdict(int)
			for k in cnt:
				for v in m[k]:
					cnt2[v] += cnt[k]
			cnt = cnt2
		return sum((cnt[k] for k in cnt)) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[1] * 10 for _ in range(n)]
		moves = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(1, n):
			for j in range(10):
				count = 0
				for digit in moves[j]:
					count += dp[i - 1][digit]
				dp[i][j] = count
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1] * 10
		for _ in range(n - 1):
			prevDp = copy.copy(dp)
			for i in range(10):
				dp[i] = sum([prevDp[move] for move in moves[i]])
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		LARGEINT = 10 ** 9 + 7
		moves = {1: 2, 2: 1, 4: 2, 7: 2, 8: 1, 0: 1}
		while n > 1:
			new_moves = {1: (moves[4] + 2 * moves[8]) % LARGEINT, 2: moves[7], 4: (moves[1] + moves[7] + 2 * moves[0]) % LARGEINT, 7: (moves[4] + 2 * moves[2]) % LARGEINT, 8: moves[1], 0: moves[4]}
			moves = new_moves
			n -= 1
		return sum(moves.values()) % LARGEINT


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		dp = [[0 for _ in range(10)] for _ in range(n + 1)]
		for r in range(n + 1):
			for c in range(10):
				if r == 0:
					dp[r][c] = 0
				elif r == 1:
					dp[r][c] = 1
				else:
					for ne in neighbors[c]:
						dp[r][c] += dp[r - 1][ne]
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

		@lru_cache(None)
		def dfs(i, n):
			if n == 1:
				return 1
			else:
				res = 0
				for c in d[i]:
					res += dfs(c, n - 1)
				return res % (10 ** 9 + 7)
		return sum((dfs(i, n) for i in range(10))) % (10 ** 9 + 7)


class Solution:

	def _knightDialer(self, n: int, curr_n: int, moves_map: dict, cache: dict) -> int:
		if n == 0:
			return 1
		if (curr_n, n) in cache:
			return cache[curr_n, n]
		distinct_nums = 0
		for next_n in moves_map[curr_n]:
			distinct_nums += self._knightDialer(n - 1, next_n, moves_map, cache)
		cache[curr_n, n] = distinct_nums
		return cache[curr_n, n]

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		mod = 10 ** 9 + 7
		moves_map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp_curr = [1] * 10
		dp_next = [0] * 10
		for _ in range(1, n):
			for (start, poss_moves) in list(moves_map.items()):
				dp_next[start] = sum((dp_curr[poss_move] for poss_move in poss_moves))
			dp_curr = dp_next
			dp_next = [0] * 10
		return sum(dp_curr) % mod


class Solution:
	adjacency = {0: {4, 6}, 1: {8, 6}, 2: {7, 9}, 3: {8, 4}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

	def knightDialer(self, n: int):
		count = [1 for _ in range(10)]
		for _ in range(n - 1):
			count = [sum((count[next_digit] for next_digit in Solution.adjacency[digit])) for digit in range(10)]
		return sum(count) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		next_move = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mod_num = 10 ** 9 + 7
		dp_prev = [1] * 10
		for i in range(n - 1):
			dp_new = [0] * 10
			for num in range(10):
				phones_for_num = sum((dp_prev[x] for x in next_move[num]))
				dp_new[num] = phones_for_num
			dp_prev = dp_new
		return sum(dp_prev) % mod_num


class Solution:

	def __init__(self):
		self.mem = dict()

	def knightDialer(self, n: int) -> int:
		reach = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		counts = [1] * 10
		for i in range(n - 1):
			counts2 = [sum((counts[k] for k in reach[j])) for j in range(10)]
			counts = counts2
		return sum(counts) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		jumps = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		if n == 1:
			return 10
		curr_total = []
		last_step_totals = [1 for _ in range(10)]
		for i in range(n - 1):
			curr_total = [0 for _ in range(10)]
			for i in range(10):
				for jump_location in jumps[i]:
					curr_total[i] += last_step_totals[jump_location]
			last_step_totals = curr_total
		return sum(curr_total) % mod


move_map = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 0, 7}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

class Solution:

	def knightDialer(self, n: int) -> int:
		table = {}
		for key in move_map:
			table[key, 1] = 1
		for N in range(2, n + 1):
			for key in move_map:
				val = 0
				for new_key in move_map[key]:
					val += table[new_key, N - 1]
				table[key, N] = val
		res = 0
		for key in move_map:
			res += table[key, n]
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		friends = [0] * 10
		friends[0] = [4, 6]
		friends[1] = [6, 8]
		friends[2] = [7, 9]
		friends[3] = [8, 4]
		friends[4] = [0, 3, 9]
		friends[5] = []
		friends[6] = [0, 1, 7]
		friends[7] = [2, 6]
		friends[8] = [1, 3]
		friends[9] = [2, 4]
		dp = [[0 for _ in range(10)] for _ in range(n + 1)]
		dp[1] = [1] * 10
		for steps in range(2, n + 1):
			for digit in range(10):
				dp[steps][digit] = sum([dp[steps - 1][f] for f in friends[digit]]) % (10 ** 9 + 7)
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		maps = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {2, 6}, 8: {1, 3}, 9: {4, 2}}
		prev = [1] * 10
		for i in range(1, n):
			curr = [0] * 10
			for j in range(0, 10):
				curr[j] = sum((prev[k] for k in maps[j]))
			prev = curr
		return sum(prev) % (10 ** 9 + 7)


possible = {-1: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
cache = {}

class Solution:

	def knightDialer(self, n: int) -> int:
		total = self.helper(-1, n, 0) % 1000000007
		return total

	def helper(self, num, n, total):
		if (num, n) in cache:
			total += cache[num, n]
			return total
		nxt = possible[num]
		total_begin = total
		if n == 1:
			total += len(nxt)
		else:
			for num_next in nxt:
				total = self.helper(num_next, n - 1, total) % 1000000007
		cache[num, n] = total - total_begin
		return total


class Solution:

	def knightDialer(self, n: int) -> int:
		moveable = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		MOD = 7 + 1000000000.0

		@lru_cache(maxsize=None)
		def helper(step, num=-1):
			if step == n:
				return 1
			result = 0
			if num == -1:
				for i in range(10):
					result = (result + helper(step + 1, i)) % MOD
			else:
				for move in moveable[num]:
					result = (result + helper(step + 1, move)) % MOD
			return result
		return int(helper(0))


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		f = [[0] * 10 for i in range(2)]
		f[1 & 1] = [1] * 10
		for i in range(2, n + 1):
			f[i & 1] = [0] * 10
			for j in range(10):
				for v in d[j]:
					f[i & 1][v] += f[i - 1 & 1][j] % (10 ** 9 + 7)
		return sum(f[n & 1]) % (10 ** 9 + 7)


possibilities = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [9, 3, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 1:
			return 10
		counter = 0
		num_ways = [1, 1, 1, 1, 1, 0, 1, 1, 1, 1]
		for i in range(N - 1):
			updated = [0] * 10
			for digit in range(10):
				updated[digit] = sum([num_ways[previous] % int(1000000000.0 + 7) for previous in possibilities[digit]])
			num_ways = updated
		return sum(num_ways) % int(1000000000.0 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		res = [1] * 10
		next_move = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		i = 1
		while i < N:
			res2 = [0] * 10
			for (k, v) in enumerate(res):
				for j in next_move[k]:
					res2[j] += v
			res = res2
			i += 1
		return sum(res) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		possible_moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [1 for _ in range(10)]
		for _ in range(1, N):
			dp1 = [0 for _ in range(10)]
			for i in range(10):
				for m in possible_moves[i]:
					dp1[i] += dp[m]
			dp = dp1
		return sum(dp) % (pow(10, 9) + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		move_dict = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		MOD = 10 ** 9 + 7
		dp = [2, 2, 2, 2, 3, 0, 3, 2, 2, 2]
		for i in range(n - 2):
			new_dp = [2, 2, 2, 2, 3, 0, 3, 2, 2, 2]
			for d in range(10):
				new_dp[d] = sum((dp[move] for move in move_dict[d])) % MOD
			dp = new_dp
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		stack = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 9], [4, 2]]
		dp = [[0 for _ in range(10)] for __ in range(n)]
		for i in range(10):
			dp[0][i] = 1
		for i in range(1, n):
			for j in range(10):
				for k in stack[j]:
					dp[i][j] = (dp[i][j] + dp[i - 1][k]) % (10 ** 9 + 7)
		return sum((dp[-1][i] for i in range(10))) % (10 ** 9 + 7)


class Solution:

	def initMoveTable(self):
		moveTable = dict()
		moveTable[0] = [4, 6]
		moveTable[1] = [6, 8]
		moveTable[2] = [7, 9]
		moveTable[3] = [4, 8]
		moveTable[4] = [0, 3, 9]
		moveTable[5] = []
		moveTable[6] = [0, 1, 7]
		moveTable[7] = [2, 6]
		moveTable[8] = [1, 3]
		moveTable[9] = [2, 4]
		return moveTable

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		if n == 1:
			return 10
		moveTable = self.initMoveTable()
		dp = []
		for i in range(n + 1):
			newRow = []
			for j in range(10):
				newRow.append(None)
			dp.append(newRow)
		for i in range(10):
			dp[1][i] = 1
		for i in range(2, n + 1):
			for j in range(10):
				localNumWays = 0
				moves = moveTable[j]
				for move in moves:
					localNumWays += dp[i - 1][move]
				dp[i][j] = localNumWays % (pow(10, 9) + 7)
		return sum(dp[i]) % (pow(10, 9) + 7)


class Solution:
	main_dic = {}

	def __init__(self):
		dic = {}
		for i in range(4):
			for j in range(3):
				if i == 3 and (j == 0 or j == 2):
					continue
				dic[i, j] = self.get_ind(i, j)
		self.main_dic = dic

	def get_ind(self, i, j):
		lst = []
		lst.append((i + 2, j - 1))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i + 2, j + 1))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i - 2, j - 1))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i - 2, j + 1))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i + 1, j + 2))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i - 1, j + 2))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i + 1, j - 2))
		if not self.check_ind(lst[-1]):
			lst.pop()
		lst.append((i - 1, j - 2))
		if not self.check_ind(lst[-1]):
			lst.pop()
		return lst

	def check_ind(self, t):
		(i, j) = t
		if i < 0 or j < 0:
			return False
		if i > 3 or j > 2:
			return False
		if i == 3 and (j == 0 or j == 2):
			return False
		return True

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		old = [[1] * 3 for i in range(4)]
		(old[3][0], old[3][2]) = (0, 0)
		for k in range(n - 1):
			new = []
			for i in range(4):
				temp = []
				for j in range(3):
					if i == 3 and (j == 0 or j == 2):
						temp.append(0)
						continue
					(lst, res) = (self.main_dic[i, j], 0)
					for (m, n) in lst:
						res += old[m][n]
					temp.append(res)
				new.append(temp)
			old = new
		res = sum([sum(l) for l in old])
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		hop_map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		memo = {(i, 1): 1 for i in range(10)}

		def num_hops(key: int, N: int):
			if N == 1:
				return 1
			if key in [1, 4, 7]:
				key += 2
			elif key == 5:
				return 0
			if (key, N) in memo:
				return memo[key, N]
			sum_ = 0
			for v in hop_map[key]:
				sum_ += num_hops(v, N - 1)
			memo[key, N] = sum_ % (10 ** 9 + 7)
			return sum_
		sum_ = 0
		for i in range(10):
			sum_ += num_hops(i, N) % (10 ** 9 + 7)
		return sum_ % (10 ** 9 + 7)


from collections import deque
MOD = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:
		m = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		curt = {i: 1 for i in range(0, 10)}
		n -= 1
		while n > 0:
			next_set = {}
			for key in curt:
				for nei in m[key]:
					next_set[nei] = (next_set.get(nei, 0) + curt[key]) % MOD
			curt = next_set
			n -= 1
		return sum(curt.values()) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) = (1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
		mod = pow(10, 9) + 7
		for i in range(n - 1):
			t0 = (x4 + x6) % mod
			t1 = (x6 + x8) % mod
			t2 = (x7 + x9) % mod
			t3 = (x4 + x8) % mod
			t4 = (x0 + x3 + x9) % mod
			t5 = 0
			t6 = (x0 + x1 + x7) % mod
			t7 = (x2 + x6) % mod
			t8 = (x1 + x3) % mod
			t9 = (x2 + x4) % mod
			(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) = (t0, t1, t2, t3, t4, t5, t6, t7, t8, t9)
		return (x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		dct = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def func(k):
			if k == 1:
				return {i: 1 for i in range(10)}
			res = func(k - 1)
			counts = {i: 0 for i in range(10)}
			for i in range(10):
				for t in dct[i]:
					counts[t] += res[i]
			return counts
		res = func(n)
		return sum(res.values()) % (10 ** 9 + 7)


from functools import lru_cache

class Solution:

	def knightDialer(self, n: int) -> int:

		@lru_cache(None)
		def jumps(start, n):
			if n == 0:
				return 1
			ans = 0
			for neighbor in neighbors[start]:
				ans = (ans + jumps(neighbor, n - 1)) % MOD
			return ans % MOD
		neighbors = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		MOD = pow(10, 9) + 7
		res = 0
		for i in range(10):
			res = (res + jumps(i, n - 1)) % MOD
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [[None] * 10 for _ in range(n)]
		for i in range(10):
			dp[0][i] = 1

		def helper(node, jumpsLeft):
			if dp[jumpsLeft][node]:
				return dp[jumpsLeft][node]
			cnt = 0
			for nextJump in moves[node]:
				cnt += helper(nextJump, jumpsLeft - 1)
				cnt %= MOD
			dp[jumpsLeft][node] = cnt
			return cnt
		for i in range(10):
			helper(i, n - 1)
		return sum(dp[n - 1]) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		nei = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		@lru_cache(None)
		def dfs(i, pre):
			if i == n:
				return 1
			cand = nei[pre] if pre != None else range(10)
			ans = 0
			for k in cand:
				ans += dfs(i + 1, k) % mod
			return ans % mod
		return dfs(0, None)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		if n == 0:
			return 0
		dp = [[1 for i in range(n)] for i in range(10)]
		for move in range(1, n):
			for num in range(10):
				dp[num][move] = sum([dp[neighbor][move - 1] for neighbor in neighbors[num]]) % 1000000007
		return sum([dp[num][n - 1] for num in range(10)]) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		w = [1]
		x = [1]
		y = [1]
		z = [1]
		for i in range(n - 1):
			w_n = 2 * x[-1]
			x_n = w[-1] + 2 * y[-1]
			y_n = x[-1] + z[-1]
			z_n = 2 * y[-1]
			w.append(w_n)
			x.append(x_n)
			y.append(y_n)
			z.append(z_n)
		return (w[-1] + 2 * x[-1] + 4 * y[-1] + 2 * z[-1] + (1 if n == 1 else 0)) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		path = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		M = 10 ** 9 + 7
		dp = [[None for _ in range(n)] for _ in range(10)]

		def paths(i, n):
			if dp[i][n]:
				return dp[i][n]
			if n == 1:
				return len(path[i])
			if n == 0:
				return 1
			s = 0
			for v in path[i]:
				s += paths(v, n - 1)
			dp[i][n] = s % M
			return dp[i][n]
		ans = 0
		for k in path:
			ans += paths(k, n - 1)
		return ans % M


class Solution:

	def knightDialer(self, n: int) -> int:
		h = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		if n == 1:
			return 10
		o = []
		le = 0
		oTrack = [0] * 10
		track = [0] * 10
		for loops in range(n - 1):
			track = [0] * 10
			for (k, v) in enumerate(track):
				hg = h.get(k)
				for i in hg:
					track[i] += max(oTrack[k], 1)
			oTrack = track.copy()
		return sum(track) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		prior_case = [1] * 10
		current_case = [1] * 10
		paths = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		curr_hop = 1
		while curr_hop < n:
			curr_hop += 1
			current_case = [0] * 10
			for num in range(10):
				for neighbor in paths[num]:
					current_case[num] += prior_case[neighbor]
			prior_case = current_case
		return sum(current_case) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mm = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [6, 4]}
		ans = 0

		@lru_cache(maxsize=None)
		def dfs(val, rem):
			if rem == 0:
				return 1
			res = 0
			for adj in mm[val]:
				res += dfs(adj, rem - 1)
			return res
		for key in list(mm.keys()):
			ans += dfs(key, n - 1)
		return ans % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0 or not n:
			return 0
		graph = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		@lru_cache(maxsize=None)
		def helper(left, curr):
			if left == 1:
				return 1
			cnt = 0
			for nei in graph[curr]:
				cnt += helper(left - 1, nei)
			return cnt
		ans = 0
		for i in range(10):
			ans += helper(n, i)
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		count = 0
		num_each_digit = {0: 1, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1, 7: 1, 8: 1, 9: 1}
		for i in range(1, n + 1):
			count = sum(num_each_digit.values())
			temp_dict = {0: 0, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0}
			for digit in num_each_digit:
				num_digit = num_each_digit[digit]
				digit_neighbors = neighbors[digit]
				for neighbor in digit_neighbors:
					temp_dict[neighbor] += num_digit
			num_each_digit = temp_dict
		return count % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:

		def matmul(A, B):
			BT = list(zip(*B))
			res = [[sum((x * y for (x, y) in zip(row, col))) % M for col in BT] for row in A]
			return res

		def pow(A, n):
			l = n.bit_length()
			res = [[1 if i == j else 0 for j in range(len(A[0]))] for i in range(len(A))]
			tmp = A
			for i in range(l):
				mask = 1 << i
				if mask & n != 0:
					res = matmul(res, tmp)
				tmp = matmul(tmp, tmp)
			return res
		M = 10 ** 9 + 7
		A = [[0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0]]
		res = matmul([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], pow(A, n - 1))
		return sum(res[0]) % M


class Solution:

	def knightDialer(self, N: int) -> int:
		numpad = [[1, 2, 3], [4, 5, 6], [7, 8, 9], ['*', 0, '#']]
		dp = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		square = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [7, 0, 1], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		for i in range(2, N + 1):
			temp = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
			for row in range(4):
				for col in range(3):
					if numpad[row][col] == '*' or numpad[row][col] == '#':
						continue
					else:
						num = numpad[row][col]
						for j in square[num]:
							temp[num] += dp[j] % mod
			dp = temp
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		from functools import lru_cache

		@lru_cache(maxsize=None)
		def dfs(i, length):
			if n == length:
				return 1
			total = 0
			for newI in moves[i]:
				total += dfs(newI, length + 1)
			return total
		bound = 10 ** 9 + 7
		ans = 0
		for i in range(0, 10):
			ans += dfs(i, 1)
			if ans >= bound:
				ans = ans % bound
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		next_moves = defaultdict(list)
		next_moves[1] = [6, 8]
		next_moves[2] = [7, 9]
		next_moves[3] = [4, 8]
		next_moves[4] = [0, 3, 9]
		next_moves[5] = []
		next_moves[6] = [0, 1, 7]
		next_moves[7] = [2, 6]
		next_moves[8] = [1, 3]
		next_moves[9] = [2, 4]
		next_moves[0] = [4, 6]
		solutions = [1 for _ in range(10)]
		while n > 1:
			next_solutions = []
			for last_num in range(0, 10):
				count = sum((solutions[prev] for prev in next_moves[last_num]))
				if count >= MOD:
					count %= MOD
				next_solutions.append(count)
			solutions = next_solutions
			n -= 1
		return sum(solutions) % MOD
		memo = dict()

		def count(size, at):
			if size == 0:
				return 1
			if (size, at) in memo:
				return memo[size, at]
			c = sum((count(size - 1, next_at) for next_at in next_moves[at]))
			if c >= MOD:
				c %= MOD
			memo[size, at] = c
			return c
		total_possible = sum((count(n - 1, at) for at in range(0, 10)))
		return total_possible % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = pow(10, 9) + 7
		maps = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [[0] * n for _ in range(10)]
		for i in range(10):
			dp[i][0] = 1
		for i in range(1, n):
			for digit in range(10):
				dp[digit][i] = sum((dp[j][i - 1] for j in maps[digit]))
		return sum((dp[digit][-1] for digit in range(10))) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		D = []
		modulo = 10 ** 9 + 7
		movesDict = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(10):
			D.append([-1] * (n + 1))

		def help(start, length):
			if length == 1:
				return 1
			if D[start][length] != -1:
				return D[start][length]
			moves = movesDict[start]
			total = 0
			for newStart in moves:
				total += help(newStart, length - 1)
				total %= modulo
			D[start][length] = total
			return total
		res = 0
		for i in range(10):
			res += help(i, n)
		return res % modulo


class Solution:

	def knightDialer(self, n: int) -> int:

		def knight_dailer(n):
			paths = {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [4, 2]}
			count = 0
			import sys, functools
			sys.setrecursionlimit(10 ** 9)

			@functools.lru_cache(None)
			def traverse(i, rem):
				if rem == 0:
					return 1
				ans = 0
				for p in paths[i]:
					res = traverse(p, rem - 1)
					ans += res
				return ans
			for i in range(10):
				count += traverse(i, n - 1)
			return count % (10 ** 9 + 7)
		return knight_dailer(n)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		map = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [1] * len(map)
		for hops in range(n - 1):
			dp2 = [0] * len(map)
			for (node, cnt) in enumerate(dp):
				for nei in map[node]:
					dp2[nei] += cnt
					dp2[nei] %= MOD
			dp = dp2
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[0] * 10 for _ in range(n)]
		pad_map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		mod = 10 ** 9 + 7
		for i in range(10):
			dp[0][i] = 1
		for i in range(n - 1):
			for j in range(10):
				dsts = pad_map[j]
				for dst in dsts:
					dp[i + 1][dst] = (dp[i][j] + dp[i + 1][dst]) % mod
		return sum(dp[-1]) % mod


class Solution:

	def knightDialer(self, N: int) -> int:
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 5: [], 0: [4, 6]}

		@lru_cache(None)
		def helper(k, i):
			if k == 0:
				return 1
			r = 0
			for n in d[i]:
				r += helper(k - 1, n)
			return r
		ans = 0
		for n in list(d.keys()):
			ans += helper(N - 1, n)
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = int(1000000000.0) + 7
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		ans = {}

		@lru_cache(maxsize=None)
		def dfs(i, n):
			nonlocal d
			if n == 0:
				return 1
			ans = 0
			for val in d[i]:
				ans += dfs(val, n - 1)
			return ans
		for i in range(10):
			if i in [3, 6, 9]:
				ans[i] = ans[i - 2]
			else:
				ans[i] = dfs(i, n - 1)
		return sum(ans.values()) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		dp = [[0 for _ in range(10)] for _ in range(n)]
		for i in range(10):
			dp[0][i] = 1

		def check(k):
			if k == 0:
				return [4, 6]
			elif k == 1:
				return [6, 8]
			elif k == 2:
				return [7, 9]
			elif k == 3:
				return [4, 8]
			elif k == 4:
				return [0, 3, 9]
			elif k == 5:
				return []
			elif k == 6:
				return [0, 1, 7]
			elif k == 7:
				return [2, 6]
			elif k == 8:
				return [1, 3]
			else:
				return [2, 4]
		for i in range(1, n):
			for j in range(10):
				for k in check(j):
					dp[i][j] = (dp[i][j] + dp[i - 1][k]) % mod
		ans = 0
		for i in range(10):
			ans = (ans + dp[n - 1][i]) % mod
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		dic = {1: [6, 8], 2: [7, 9], 4: [0, 3, 9], 5: [], 7: [2, 6], 8: [1, 3], 0: [4, 6]}
		pair = {3: 1, 6: 4, 9: 7}

		@lru_cache(None)
		def dp(i, n):
			if n == 1:
				return 1
			if i in pair:
				i = pair[i]
			res = 0
			for j in dic[i]:
				res += dp(j, n - 1)
			return res
		return (2 * (dp(1, n) + dp(4, n) + dp(7, n)) + dp(0, n) + dp(2, n) + dp(5, n) + dp(8, n)) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		valid_moves = {0: (4, 6), 1: (8, 6), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		dp = [[0] * 10 for _ in range(n)]
		for c in range(10):
			dp[0][c] = 1
		if n > 1:
			for c in range(10):
				dp[1][c] = len(valid_moves[c])
		for i in range(2, n):
			for j in range(10):
				valid = valid_moves[j]
				dp[i][j] = sum([dp[i - 1][r] for r in valid])
		return sum(dp[n - 1]) % (10 ** 9 + 7)


class Solution:
	legal_moves = {0: [4, 4], 1: [6, 8], 2: [7, 7], 3: [4, 8], 4: [0, 1, 7], 6: [0, 1, 7], 7: [2, 4], 8: [1, 1], 9: [2, 4]}

	def knightDialer(self, n: int) -> int:
		total = 0 if n != 1 else 1
		memo = {}
		for i in range(0, 10):
			if i is not 5:
				total = total + self.num_jumps(i, n - 1, memo)
		return total % (pow(10, 9) + 7)

	def num_jumps(self, start, jumps_left, memo):
		if jumps_left == 0:
			return 1
		if (start, jumps_left) not in memo:
			total = 0
			for legal_move in self.legal_moves[start]:
				total = total + self.num_jumps(legal_move, jumps_left - 1, memo)
			memo[start, jumps_left] = total
		return memo[start, jumps_left]


from functools import lru_cache

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4)}

		@lru_cache(maxsize=None)
		def num_ways(key, n):
			if n == 0:
				return 0
			if n == 1:
				return len(neighbors[key])
			w = 0
			for neighbor in neighbors[key]:
				w += num_ways(neighbor, n - 1)
			return w
		answer = 0
		for i in range(10):
			answer += num_ways(i, n - 1)
		answer %= pow(10, 9) + 7
		return answer


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		ret = 0
		dp = [[0] * 10 for i in range(n)]
		for i in range(10):
			dp[0][i] = 1
		graph = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(1, n):
			for j in range(10):
				for neighbor in graph[j]:
					dp[i][j] += dp[i - 1][neighbor]
		ret = sum((dp[n - 1][i] for i in range(10)))
		return ret % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		knight_graph = {1: (8, 6), 2: (7, 9), 3: (8, 4), 4: (3, 9, 0), 5: (), 6: (7, 1, 0), 7: (2, 6), 8: (1, 3), 9: (4, 2), 0: (4, 6)}
		memo = {}
		MOD = pow(10, 9) + 7

		def btHelper(coordinate, n):
			if n == 0:
				return 1
			possibility = 0
			for avail_node in knight_graph[coordinate]:
				if (avail_node, n - 1) in memo:
					possibility += memo[avail_node, n - 1]
				else:
					possibility += btHelper(avail_node, n - 1)
			memo[coordinate, n] = possibility % MOD
			return possibility
		ans = 0
		for i in range(10):
			ans += btHelper(i, n - 1)
		return ans % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9) = (1, 1, 1, 1, 1, 0, 1, 1, 1, 1)
		for i in range(1, n):
			(x0, x1, x2, x3, x4, x6, x7, x8, x9) = (x4 + x6, x6 + x8, x7 + x9, x4 + x8, x0 + x3 + x9, x0 + x1 + x7, x2 + x6, x1 + x3, x2 + x4)
		return (x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x0) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		cell2jump = dict()
		cell2jump[1] = [6, 8]
		cell2jump[2] = [7, 9]
		cell2jump[3] = [4, 8]
		cell2jump[4] = [3, 9, 0]
		cell2jump[5] = []
		cell2jump[6] = [1, 7, 0]
		cell2jump[7] = [2, 6]
		cell2jump[8] = [1, 3]
		cell2jump[9] = [2, 4]
		cell2jump[0] = [4, 6]
		dp = [1] * 10
		for _ in range(n - 1):
			new_dp = [0] * 10
			for i in range(10):
				new_dp[i] = sum((dp[nxt] for nxt in cell2jump[i]))
			dp = new_dp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		kd_key = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		memo = dict()
		out = 0
		for i in range(10):
			out += self.dial(i, n, kd_key, memo)
		return out % int(1000000000.0 + 7)

	def dial(self, pos, n, kd_key, memo):
		if n == 1:
			return 1
		out = 0
		for next_pos in kd_key[pos]:
			if (next_pos, n - 1) in memo:
				out += memo[next_pos, n - 1]
			else:
				out += self.dial(next_pos, n - 1, kd_key, memo)
		memo[pos, n] = out
		return out


class Solution:

	def knightDialer(self, n: int) -> int:
		jump = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		memo = {}

		def helper(cur, k):
			if (cur, k) in memo:
				return memo[cur, k]
			if k == 0:
				return 0
			elif k == 1:
				return 1
			res = 0
			for item in jump[cur]:
				res += helper(item, k - 1)
			memo[cur, k] = res % (10 ** 9 + 7)
			return res
		res = 0
		for i in range(10):
			res += helper(i, n)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		p = math.pow(10, 9) + 7
		c = {}
		c[1] = [6, 8]
		c[2] = [7, 9]
		c[3] = [4, 8]
		c[4] = [3, 9, 0]
		c[5] = []
		c[6] = [1, 7, 0]
		c[7] = [2, 6]
		c[8] = [1, 3]
		c[9] = [2, 4]
		c[0] = [4, 6]
		dp = [[None for _ in range(n + 1)] for _ in range(10)]
		for i in range(10):
			dp[i][1] = 1
			dp[i][2] = len(c[i])

		def find(i, x):
			if dp[i][x] is not None:
				return dp[i][x]
			dp[i][x] = 0
			for j in c[i]:
				dp[i][x] += find(j, x - 1) % p
			return dp[i][x]
		res = 0
		for i in range(10):
			res += find(i, n) % p
		return int(res % p)


class Solution:

	def knightDialer(self, N: int) -> int:
		numpad = [[1, 2, 3], [4, 5, 6], [7, 8, 9], ['*', 0, '#']]
		dp = [1] * 10
		square = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [7, 0, 1], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		for i in range(2, N + 1):
			temp = [0] * 10
			for num in range(10):
				for j in square[num]:
					temp[num] += dp[j] % mod
			dp = temp
		return sum(dp) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [6, 4]}
		p = 10 ** 9 + 7
		dp = defaultdict(lambda : 1)
		for t in range(n - 1):
			for i in range(10):
				dp[i, t & 1] = sum((dp[j, t + 1 & 1] for j in neighbors[i])) % p
		return sum((dp[i, n & 1] for i in range(10))) % p


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[] for x in range(10)]
		moves[0] = [4, 6]
		moves[1] = [6, 8]
		moves[2] = [7, 9]
		moves[3] = [4, 8]
		moves[4] = [3, 9, 0]
		moves[5] = []
		moves[6] = [0, 1, 7]
		moves[7] = [2, 6]
		moves[8] = [1, 3]
		moves[9] = [2, 4]
		dp = {}

		def dialer(start, n):
			if (start, n) in dp:
				return dp[start, n]
			if n == 1:
				dp[start, n] = 1
				return 1
			xmoves = 0
			for move in moves[start]:
				xmoves += dialer(move, n - 1)
			xmoves %= 10 ** 9 + 7
			dp[start, n] = xmoves
			return xmoves
		xmoves = 0
		for i in range(10):
			xmoves += dialer(i, n)
		return xmoves % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:

		@lru_cache(None)
		def dp(i, k):
			if k == 0:
				return 1
			result = 0
			for j in jump[i]:
				result = (result + dp(j, k - 1)) % MOD
			return result
		MOD = 10 ** 9 + 7
		jump = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [0, 1, 7], [2, 6], [1, 3], [2, 4], list(range(10))]
		return dp(10, n)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		list_old = [1] * 10
		for t in range(2, n + 1):
			list_new = [0] * 10
			for i in range(0, 10):
				temp = Solution().map(i)
				for j in range(len(temp)):
					list_new[i] = list_new[i] + list_old[temp[j]]
			list_old = list_new[0:10]
		return sum(list_old) % (10 ** 9 + 7)

	def map(self, d: int) -> List[int]:
		if d == 0:
			return [4, 6]
		elif d == 1:
			return [6, 8]
		elif d == 2:
			return [7, 9]
		elif d == 3:
			return [4, 8]
		elif d == 4:
			return [0, 3, 9]
		elif d == 5:
			return []
		elif d == 6:
			return [0, 1, 7]
		elif d == 7:
			return [2, 6]
		elif d == 8:
			return [1, 3]
		else:
			return [2, 4]


class Solution:

	def knightDialer(self, n: int) -> int:
		G = {5: set(), 1: set([6, 8]), 3: set([4, 8]), 7: set([2, 6]), 9: set([2, 4]), 4: set([3, 9, 0]), 6: set([1, 7, 0]), 2: set([7, 9]), 8: set([1, 3]), 0: set([4, 6])}
		mem = dict()

		def dfs(val, rem):
			if (val, rem) in mem:
				return mem[val, rem]
			if rem == 1:
				return 1
			ans = 0
			for n in G[val]:
				ans += dfs(n, rem - 1)
			mem[val, rem] = ans
			return ans % (10 ** 9 + 7)
		ans = 0
		for i in range(10):
			ans += dfs(i, n)
		return ans % (10 ** 9 + 7)


from collections import defaultdict
move_map = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 0, 7}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

class Solution:

	def knightDialer(self, n: int) -> int:
		table = defaultdict(int)
		for key in move_map:
			table[key, 1] = 1
		for N in range(2, n + 1):
			for key in move_map:
				for new_key in move_map[key]:
					table[key, N] += table[new_key, N - 1]
		res = 0
		for key in move_map:
			res += table[key, n]
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		map = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		memo = [[-1] * n for i in range(len(map))]

		def recur(num, hops, memo):
			if hops < 0:
				return 0
			elif hops == 0:
				return 1
			if memo[num][hops] == -1:
				s = 0
				for move in map[num]:
					s += recur(move, hops - 1, memo)
				memo[num][hops] = s
			return memo[num][hops]
		s = 0
		for key in range(len(map)):
			s += recur(key, n - 1, memo)
		return s % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		R = int(math.pow(10, 9) + 7)
		memo = {}
		options = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}

		def dfs(step, dig):
			if (step, dig) in memo:
				return memo[step, dig]
			if step == 1:
				return 1
			res = 0
			for d in options[dig]:
				res = (res + dfs(step - 1, d)) % R
			memo[step, dig] = res
			return res
		res = 0
		for d in range(0, 10, 1):
			if d == 5:
				continue
			res = (res + dfs(n, d)) % R
		return res


class Solution:

	def knightDialer(self, N: int) -> int:
		dp = {}
		MOD = 10 ** 9 + 7

		def moveOnce(num0, N0):
			if (num0, N0) in dp:
				return dp[num0, N0]
			if N0 == 0:
				return 1
			if N0 < 0:
				return 0
			subAns = 0
			if num0 == 1:
				subAns = moveOnce(6, N0 - 1) + moveOnce(8, N0 - 1)
			elif num0 == 2:
				subAns = moveOnce(7, N0 - 1) + moveOnce(9, N0 - 1)
			elif num0 == 3:
				subAns = moveOnce(4, N0 - 1) + moveOnce(8, N0 - 1)
			elif num0 == 4:
				subAns = moveOnce(3, N0 - 1) + moveOnce(9, N0 - 1) + moveOnce(0, N0 - 1)
			elif num0 == 5:
				subAns = 0
			elif num0 == 6:
				subAns = moveOnce(1, N0 - 1) + moveOnce(7, N0 - 1) + moveOnce(0, N0 - 1)
			elif num0 == 7:
				subAns = moveOnce(2, N0 - 1) + moveOnce(6, N0 - 1)
			elif num0 == 8:
				subAns = moveOnce(1, N0 - 1) + moveOnce(3, N0 - 1)
			elif num0 == 9:
				subAns = moveOnce(2, N0 - 1) + moveOnce(4, N0 - 1)
			elif num0 == 0:
				subAns = moveOnce(4, N0 - 1) + moveOnce(6, N0 - 1)
			dp[num0, N0] = subAns % MOD
			return subAns
		return sum([moveOnce(i, N - 1) for i in range(10)]) % MOD


class Solution:

	def knightDialer(self, N: int) -> int:

		def getNeighbors(N):
			neighs = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
			return neighs[N]
		mod = 10 ** 9 + 7
		curr = [1] * 10
		for i in range(N - 1):
			nextlist = [0] * 10
			for j in range(10):
				for neigh in getNeighbors(j):
					nextlist[neigh] = (nextlist[neigh] + curr[j]) % mod
			curr = nextlist
		return sum(curr) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		jumps = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		dp = [1] * 10
		for i in range(2, n + 1):
			t = list(dp)
			for i in range(10):
				dp[i] = sum((t[v] for v in jumps[i])) % MOD
		return sum(dp) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		last_dp = [1] * 10
		this_dp = [0] * 10
		next_steps = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		for _ in range(2, n + 1):
			for i in range(10):
				if i != 5:
					this_dp[i] = sum((last_dp[next_step] for next_step in next_steps[i])) % int(10 ** 9 + 7)
			last_dp = this_dp
			this_dp = [0] * 10
		return sum(last_dp) % int(10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		graph = {1: (6, 8), 2: (9, 7), 3: (4, 8), 4: (9, 3, 0), 5: (), 6: (7, 1, 0), 7: (2, 6), 8: (1, 3), 9: (4, 2), 0: (4, 6)}
		count = 0
		MOD = 10 ** 9 + 7
		memo = collections.defaultdict(list)

		def dfs(cur, graph, n, memo):
			if n == 0:
				return 1
			if (n, cur) in memo:
				return memo[n, cur]
			count = 0
			for nei in graph[cur]:
				count += dfs(nei, graph, n - 1, memo) % MOD
			memo[n, cur] = count
			return count
		for nei in range(10):
			memo[nei] = []
			count += dfs(nei, graph, n - 1, memo) % MOD
		return count % MOD


class Solution:

	def knightDialer(self, N: int) -> int:
		memo = {}
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		for i in range(0, 10):
			memo[i, 0] = 0
			memo[i, 1] = 1
		for n in range(2, N + 1):
			for i in range(0, 10):
				memo[i, n] = 0
				for nextDig in moves[i]:
					memo[i, n] += memo[nextDig, n - 1]
		total = 0
		for i in range(0, 10):
			total += memo[i, N]
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		s = 0
		for k in range(10):
			d = [0] * 10
			d[k] = 1
			for i in range(n - 1):
				d2 = [d[4] + d[6], d[6] + d[8], d[7] + d[9], d[4] + d[8], d[3] + d[9] + d[0], 0, d[1] + d[7] + d[0], d[2] + d[6], d[1] + d[3], d[2] + d[4]]
				d = d2
			s += sum(d)
		return s % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		nei = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

		def helper(n, curr, seen, nei):
			if n == 1:
				return 1
			if curr not in nei:
				return 0
			key = (n, curr)
			if key in seen:
				return seen[key]
			answer = 0
			for ne in nei[curr]:
				answer = (answer + helper(n - 1, ne, seen, nei)) % (10 ** 9 + 7)
			seen[key] = answer
			return answer
		total = 0
		seen = {}
		for i in range(10):
			total = (total + helper(n, i, seen, nei)) % (10 ** 9 + 7)
		return total


class Solution:

	def knightDialer(self, N: int) -> int:
		mapping = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		if N == 1:
			return 10
		dp = collections.defaultdict(int)
		for idx in range(10):
			if idx == 5:
				continue
			dp[idx] = 1
		while N > 1:
			next_dp = collections.defaultdict(int)
			for idx in range(10):
				if idx == 5:
					continue
				for k in mapping[idx]:
					next_dp[k] += dp[idx]
			N -= 1
			dp = next_dp
		return sum(dp.values()) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		validNumbers = {(1, i): 1 for i in range(10)}
		BIG_MOD = 10 ** 9 + 7

		def computePhoneNumbers(length, startDigit):
			if (length, startDigit) in validNumbers:
				return validNumbers[length, startDigit]
			else:
				totalValid = 0
				for neighbor in neighbors[startDigit]:
					totalValid += computePhoneNumbers(length - 1, neighbor)
					totalValid %= BIG_MOD
				validNumbers[length, startDigit] = totalValid
				return totalValid
		allValid = 0
		for i in range(10):
			allValid += computePhoneNumbers(n, i)
			allValid %= BIG_MOD
		return allValid


from collections import defaultdict

class Solution:

	def knightDialer(self, n: int) -> int:
		self.buildPad()
		self.buildMoves()
		self.memo = [[-1 for _ in range(n)] for _ in range(10)]
		numbers = sum((self.visit(start, n - 1) for start in range(10)))
		return numbers % (10 ** 9 + 7)

	def visit(self, start: int, n: int) -> int:
		if n == 0:
			return 1
		elif self.memo[start][n] != -1:
			return self.memo[start][n]
		numbers = 0
		for new_start in self.moves[start]:
			numbers += self.visit(new_start, n - 1)
		self.memo[start][n] = numbers
		return numbers

	def buildPad(self) -> None:
		self.pad = [[str(i + j) for j in range(3)] for i in range(1, 10, 3)]
		self.pad.append(['*', '0', '#'])

	def buildMoves(self) -> None:
		self.moves = ((4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4))


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 1:
			return 10
		mapper = {1: [8, 6], 2: [7, 9], 3: [8, 4], 4: [0, 9, 3], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [[0] * 10 for _ in range(N)]
		MM = 10 ** 9 + 7
		for i in range(10):
			if i == 5:
				continue
			dp[0][i] = 1

		def searching(s, i):
			if dp[s][i] > 0:
				return dp[s][i]
			for k in mapper[i]:
				dp[s][i] += searching(s - 1, k)
				dp[s][i] = dp[s][i] % MM
			return dp[s][i]
		for i in range(10):
			if i == 5:
				continue
			searching(N - 1, i)
		return sum(dp[N - 1]) % MM


class Solution:

	def knightDialer(self, n: int) -> int:
		possibleMoves = {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		upper = 10 ** 9 + 7
		cache = {}

		def dfs(steps, loc):
			if (steps, loc) in cache:
				return cache[steps, loc]
			if steps == 0:
				return 1
			ans = 0
			for stop in possibleMoves[loc]:
				ans = (ans + dfs(steps - 1, stop)) % upper
			cache[steps, loc] = ans
			return ans
		return sum((dfs(n - 1, loc) for loc in possibleMoves)) % upper


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		if n == 1:
			return 10
		moves = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = dict()

		def count_moves(position, digits):
			if digits == 1:
				return 1
			if (position, digits) in memo:
				return memo[position, digits]
			curr = 0
			for m in moves[position]:
				curr += count_moves(m, digits - 1)
			memo[position, digits] = curr % MOD
			return memo[position, digits]
		res = 0
		for pos in moves.keys():
			res += count_moves(pos, n)
			res %= MOD
		return res


class Solution:

	def knightDialer(self, N: int) -> int:
		MOD = 10 ** 9 + 7
		reach = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = {}

		def helper(num, steps):
			if (num, steps) in memo:
				return memo.get((num, steps))
			if steps == 0:
				memo[num, steps] = 1
				return memo.get((num, steps))
			res = 0
			for next_no in reach[num]:
				res += helper(next_no, steps - 1)
			res = res % MOD
			memo[num, steps] = res
			return res
		result = 0
		for pos in range(0, 10):
			result += helper(pos, N - 1)
		return result % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		paths = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		counts = 0
		lookup = {}
		for i in range(10):
			counts += self.traverse(i, paths, lookup, n, 0)
		return counts % (10 ** 9 + 7)

	def traverse(self, starting, paths, lookup, n, level):
		if level == n - 1:
			return 1
		counts = 0
		for path in paths[starting]:
			if (path, level + 1) not in lookup:
				lookup[path, level + 1] = self.traverse(path, paths, lookup, n, level + 1)
			counts += lookup[path, level + 1]
		return counts % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		adj_graph = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}

		def moveHelper(num, n, memo):
			if n == 1:
				return 1
			sumCounts = 0
			for number in adj_graph[num]:
				if (number, n - 1) in memo:
					sumCounts += memo[number, n - 1]
				else:
					res = moveHelper(number, n - 1, memo)
					sumCounts += res
					memo[number, n - 1] = res
			return sumCounts
		sumCount = 0
		memo = {}
		for k in list(adj_graph.keys()):
			sumCount += moveHelper(k, n, memo)
		return sumCount % (pow(10, 9) + 7)


import numpy as np

class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10

		def fast_power(a, m):
			res = np.identity(10, int)
			for (bit_idx, bit) in enumerate(reversed(bin(m)[2:])):
				if bit_idx == 0:
					cur = a
				else:
					cur = np.mod(np.dot(cur, cur), 10 ** 9 + 7)
				if bit == '1':
					res = np.mod(np.dot(res, cur), 10 ** 9 + 7)
			return res
		gh = {}
		gh[0] = [4, 6]
		gh[1] = [6, 8]
		gh[2] = [7, 9]
		gh[3] = [4, 8]
		gh[4] = [0, 3, 9]
		gh[5] = []
		gh[6] = [0, 1, 7]
		gh[7] = [2, 6]
		gh[8] = [1, 3]
		gh[9] = [2, 4]
		t = []
		for u in gh:
			if u != 5:
				row = 0
				for v in gh[u]:
					row = row ^ 1 << v
				row = list(bin(row)[2:])
				row.reverse()
				row = list([int(x) for x in row])
				row.extend([0] * (10 - len(row)))
				t.append(row)
			else:
				t.append([0] * 10)
		t = np.array(t, dtype=int)
		ans = sum(np.mod(np.dot(fast_power(t, n - 1), np.ones(10, dtype=int)), 10 ** 9 + 7)) % (10 ** 9 + 7)
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		modulo = pow(10, 9) + 7
		get_position = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		cache = {}

		def solve(pos, step):
			key = (pos, step)
			if key not in cache:
				if step >= n:
					return 1
				res = 0
				for i in get_position[pos]:
					res += solve(i, step + 1)
					res = res % modulo
				cache[key] = res
			return cache[key]
		res = 0
		for i in range(10):
			res += solve(i, 1)
		return res % modulo


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		reachFrom = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [[1] * 10 for _ in range(2)]
		for i in range(1, n):
			for j in range(10):
				dp[i % 2][j] = 0
				for src in reachFrom[j]:
					dp[i % 2][j] += dp[(i - 1) % 2][src]
		return sum(dp[(n - 1) % 2]) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		valid = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}
		MOD = 10 ** 9 + 7
		dp = {}
		nums = 0

		def dfs(pos, steps):
			if steps == 0:
				return 1
			if (pos, steps) in dp:
				return dp[pos, steps]
			c = 0
			for next in valid[pos]:
				c += dfs(next, steps - 1)
				c %= MOD
			dp[pos, steps] = c
			return c
		ans = 0
		for i in range(10):
			x = dfs(i, n - 1)
			ans += x
			ans %= MOD
		return ans % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		self.knight_movable_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		self.dp = [[None for _ in range(10)] for _ in range(n)]

		def traverse(dial, remaining):
			if remaining == 0:
				return 1
			if self.dp[remaining][dial] is not None:
				return self.dp[remaining][dial]
			cnt = 0
			for next_dial in self.knight_movable_map[dial]:
				cnt += traverse(next_dial, remaining - 1)
			self.dp[remaining][dial] = cnt
			return cnt
		cnt = 0
		for i in range(10):
			cnt += traverse(i, n - 1)
		modulo_num = 10 ** 9 + 7
		return cnt % modulo_num


class Solution:

	def knightDialer(self, N: int) -> int:
		steps = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def dfs(start, remain, seen):
			if remain == 0:
				return 1
			if (start, remain) in seen:
				return seen[start, remain]
			ans = 0
			for s in steps[start]:
				ans += dfs(s, remain - 1, seen)
			seen[start, remain] = ans
			return ans
		ans = 0
		seen = {}
		for i in range(10):
			ans += dfs(i, N - 1, seen)
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: [], 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		memo = {}

		def dp_memo(S, N):
			if (S, N) in memo:
				return memo[S, N]
			elif N == 0:
				return 1
			else:
				moves = 0
				for neigh in neighbors[S]:
					moves += dp_memo(neigh, N - 1)
				memo[S, N] = moves
				return moves
		result = 0
		for i in range(0, 10):
			result += dp_memo(i, n - 1)
		return result % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		mem = {}
		MOD = 10 ** 9 + 7

		def get(start, k):
			if k == 1:
				return 1
			if (start, k) in mem:
				return mem[start, k]
			total = 0
			for nxt in moves[start]:
				total += get(nxt, k - 1)
				total = total % MOD
			mem[start, k] = total
			return total
		ret = 0
		for x in range(10):
			ret += get(x, n)
			ret = ret % MOD
		return ret


class Solution:

	def knightDialer(self, n: int) -> int:
		mapping = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = {}

		def helper(num, total):
			if (num, total) in memo:
				return memo[num, total]
			if total == 0:
				return 1
			count = 0
			for next_num in mapping[num]:
				count += helper(next_num, total - 1)
			memo[num, total] = count
			return count
		count = 0
		for i in range(10):
			count += helper(i, n - 1)
		return count % (10 ** 9 + 7)


class Solution:

	def __init__(self):
		self.moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [7, 1, 0], [6, 2], [1, 3], [4, 2]]
		self.memoized_moves = {}

	def knightDialer(self, n: int) -> int:
		moves = 0
		for i in range(10):
			moves += self.getNumberFromNMoves(n - 1, i)
		return moves % (pow(10, 9) + 7)

	def getNumberFromNMoves(self, remaining_moves, current_number):
		if remaining_moves == 0:
			return 1
		moves = 0
		for move in self.moves[current_number]:
			if (move, remaining_moves) not in self.memoized_moves:
				self.memoized_moves[move, remaining_moves] = self.getNumberFromNMoves(remaining_moves - 1, move)
			moves += self.memoized_moves[move, remaining_moves]
		return moves

	def getMoves(self, number):
		return self.moves[number]


class Solution:

	def knightDialer(self, n: int) -> int:
		c = 0
		mp = [[4, 6], [6, 8], [9, 7], [8, 4], [0, 9, 3], [], [1, 7, 0], [6, 2], [3, 1], [2, 4]]
		memo = {}
		for i in range(0, 10):
			c += self.gen(i, n, mp, memo)
		mpow = 10 ** 9 + 7
		return c % mpow

	def gen(self, start, n, mp, memo):
		if n == 1:
			return 1
		key = (start, n)
		if key in memo:
			return memo[key]
		c = 0
		for opt in mp[start]:
			c += self.gen(opt, n - 1, mp, memo)
		memo[key] = c
		return c


class Solution:

	def distinctNumbers(self, start, moves, validMoves, cache):
		if moves == 1:
			return 1
		if (start, moves) in cache:
			return cache[start, moves]
		result = 0
		for i in validMoves[start]:
			result += self.distinctNumbers(i, moves - 1, validMoves, cache)
		cache[start, moves] = result
		return result

	def knightDialer(self, n: int) -> int:
		validMoves = dict()
		validMoves[1] = [6, 8]
		validMoves[2] = [7, 9]
		validMoves[3] = [4, 8]
		validMoves[4] = [3, 9, 0]
		validMoves[5] = []
		validMoves[6] = [1, 7, 0]
		validMoves[7] = [2, 6]
		validMoves[8] = [1, 3]
		validMoves[9] = [2, 4]
		validMoves[0] = [4, 6]
		cache = {}
		result = 0
		for i in range(10):
			result += self.distinctNumbers(i, n, validMoves, cache)
		return result % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		self.res = 0
		mapping = {1: [6, 8], 2: [9, 7], 3: [8, 4], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6], 5: []}
		memo = {}

		def helper(n, rem):
			if (n, rem) in memo:
				return memo[n, rem]
			if rem == 0:
				return 1
			res = 0
			for nei in mapping[n]:
				res += helper(nei, rem - 1)
			memo[n, rem] = res
			return res
		res = 0
		for i in range(10):
			res += helper(i, n - 1)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def helper(pos, hops_left):
			if hops_left == 1:
				return 1
			if (pos, hops_left) in cache:
				return cache[pos, hops_left]
			else:
				sequences = 0
				for ne in neighbors[pos]:
					sequences += helper(ne, hops_left - 1)
				cache[pos, hops_left] = sequences
				return sequences
		cache = {}
		counts = [0] * 10
		for start in range(10):
			counts[start] = helper(start, n)
		return sum(counts) % (10 ** 9 + 7)


class Solution:
	moves = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

	def dialed_Numbers(self, number, moves_left, memoization):
		if (number, moves_left) in memoization:
			return memoization[number, moves_left]
		if moves_left == 0:
			return 1
		fin_sum = 0
		for next_move in self.moves[number]:
			fin_sum += self.dialed_Numbers(next_move, moves_left - 1, memoization)
		memoization[number, moves_left] = fin_sum
		return fin_sum

	def knightDialer(self, n: int) -> int:
		memoization = {}
		fin_sum = 0
		for i in range(0, 10):
			fin_sum += self.dialed_Numbers(i, n - 1, memoization)
		return fin_sum % (10 ** 9 + 7)


class Solution:

	def recur_helper(self, num, n, cnt, memo, next_moves):
		if n == 0:
			return cnt
		key = (num, n)
		if key in memo:
			return memo[key]
		cnt = 0
		for next_num in next_moves[num]:
			cnt += self.recur_helper(next_num, n - 1, 1, memo, next_moves)
		memo[key] = cnt
		return memo[key]

	def knightDialer(self, n: int) -> int:
		next_moves = {0: [4, 6], 1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [9, 3, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = dict()
		cnt = 0
		for num in range(10):
			cnt += self.recur_helper(num, n - 1, 1, memo, next_moves)
		return cnt % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		results = 0
		self.cache = {}
		for pos in range(10):
			results += self.traverse(pos, n)
			results %= 1000000007
		return results

	def traverse(self, pos: int, length: int) -> int:
		if length == 1:
			return 1
		if (pos, length) in self.cache:
			return self.cache[pos, length]
		jumps = 0
		for neighbor in self.get_neighbors(pos):
			jumps += self.traverse(neighbor, length - 1)
		jumps %= 1000000007
		self.cache[pos, length] = jumps
		return jumps

	def get_neighbors(self, n: int) -> Tuple[int]:
		NEIGHBORS = ((4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4))
		return NEIGHBORS[n]


class Solution:

	def knightDialer(self, n: int) -> int:
		self.edges = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [9, 3, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		self.MAX = 10 ** 9 + 7
		self.ledger = [[None] * n for _ in range(10)]
		dialable = 0
		for cell in range(10):
			dialable += self.knight_dialer(n - 1, cell)
		return dialable % self.MAX

	def knight_dialer(self, steps_left: int, position: int) -> None:
		if not steps_left:
			return 1
		if self.ledger[position][steps_left]:
			return self.ledger[position][steps_left]
		dialable = 0
		for nbr in self.edges[position]:
			dialable += self.knight_dialer(steps_left - 1, nbr) % self.MAX
		self.ledger[position][steps_left] = dialable
		return dialable % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		graph = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

		@lru_cache(None)
		def dfs(node, n=n):
			if n == 1:
				return 1
			else:
				moves = 0
				for neigb in graph[node]:
					moves += dfs(neigb, n - 1)
				return moves
		ans = 0
		for node in range(10):
			ans += dfs(node)
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbours = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		memo = {}

		def helper(position, num_hops):
			if (position, num_hops) in memo:
				return memo[position, num_hops]
			if num_hops == 0:
				return 1
			num_sequences = 0
			for neighbour in neighbours[position]:
				num_sequences += helper(neighbour, num_hops - 1)
			memo[position, num_hops] = num_sequences
			return num_sequences
		total = 0
		for pos in neighbours:
			total += helper(pos, n - 1)
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [[-1 for i in range(n + 1)] for i in range(10)]
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		out = 0
		for i in range(0, 10):
			out += self.helper(n - 1, i, d, dp)
		return out % 1000000007

	def helper(self, n, index, d, dp):
		if n == 0:
			return 1
		if dp[index][n] != -1:
			return dp[index][n]
		ans = 0
		for i in range(len(d[index])):
			ans += self.helper(n - 1, d[index][i], d, dp)
		dp[index][n] = ans
		return ans


class Solution:
	mod = 10 ** 9 + 7

	def knightDialer(self, N: int) -> int:
		nMap = {0: (6, 4), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (4, 2)}
		m = {}

		def count(start, n):
			if (start, n) in m:
				return m[start, n]
			if n == 0:
				return 1
			else:
				num = 0
				for i in nMap[start]:
					num += count(i, n - 1)
				m[start, n] = num
				return num
		ret = 0
		for i in range(10):
			ret = (ret + count(i, N - 1)) % self.mod
		return int(ret)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		cache = {}

		def backtrack(pos, hops):
			if (pos, hops) in cache:
				return cache[pos, hops]
			if hops == 0:
				return 1
			count = 0
			for nbr in moves[pos]:
				count += backtrack(nbr, hops - 1)
			cache[pos, hops] = count
			return count
		counts = 0
		for pos in range(10):
			counts += backtrack(pos, n - 1)
		return counts % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moveMap = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}
		memo = {}

		def aux(key, rem):
			if rem == 0:
				return 1
			if (key, rem) in memo:
				return memo[key, rem]
			count = 0
			moves = moveMap[key]
			for m in moves:
				count += aux(m, rem - 1)
			memo[key, rem] = count
			return count
		count = 0
		for startKey in moveMap:
			count += aux(startKey, n - 1)
		return count % MOD


class Solution:

	def __init__(self):
		self.pos_2_pos_map = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 0, 9), 5: tuple(), 6: (7, 1, 0), 7: (2, 6), 8: (1, 3), 9: (4, 2), 0: (4, 6)}

	def dfs(self, position, n, memo):
		if n == 0:
			return 1
		if (position, n) in memo:
			return memo[position, n]
		counts = 0
		for nei in self.pos_2_pos_map[position]:
			counts += self.dfs(nei, n - 1, memo)
		memo[position, n] = counts
		return counts

	def knightDialer(self, n: int) -> int:
		memo = {}
		counts = 0
		for position in self.pos_2_pos_map:
			counts += self.dfs(position, n - 1, memo)
		return counts % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, l: int) -> int:
		table = defaultdict(lambda : defaultdict(int))
		tableEnts = {(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (5, 0), (6, 0), (7, 0), (8, 0), (9, 0)}

		def dp(n, lv) -> int:
			if lv == 0:
				return 1
			if (n, lv) in tableEnts:
				return table[n][lv]
			if n == 0:
				ret = dp(4, lv - 1) + dp(6, lv - 1)
			elif n == 1:
				ret = dp(6, lv - 1) + dp(8, lv - 1)
			elif n == 2:
				ret = dp(7, lv - 1) + dp(9, lv - 1)
			elif n == 3:
				ret = dp(4, lv - 1) + dp(8, lv - 1)
			elif n == 4:
				ret = dp(3, lv - 1) + dp(9, lv - 1) + dp(0, lv - 1)
			elif n == 6:
				ret = dp(1, lv - 1) + dp(7, lv - 1) + dp(0, lv - 1)
			elif n == 7:
				ret = dp(2, lv - 1) + dp(6, lv - 1)
			elif n == 8:
				ret = dp(1, lv - 1) + dp(3, lv - 1)
			elif n == 9:
				ret = dp(2, lv - 1) + dp(4, lv - 1)
			ret %= 1000000007
			table[n][lv] = ret
			tableEnts.add((n, lv))
			return ret
		if l == 1:
			return 10
		else:
			res = 0
			for i in [0, 1, 2, 3, 4, 6, 7, 8, 9]:
				res += dp(i, l - 1)
			return res % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		k = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mem = {}

		def count(i, j):
			if j > n:
				return 0
			if j == n:
				return 1
			if (i, j) in mem:
				return mem[i, j]
			cc = 0
			for l in k[i]:
				cc += count(l, j + 1)
			mem[i, j] = cc % (10 ** 9 + 7)
			return mem[i, j]
		return sum((count(i, 1) for i in range(10))) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		cnt = 0
		jump = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		visited = dict()

		def helper(n, i):
			if (n, i) in visited:
				return visited[n, i]
			if n == 1:
				visited[n, i] = 1
				return 1
			tot = 0
			for v in jump[i]:
				tot += helper(n - 1, v)
			visited[n, i] = tot
			return tot
		for i in range(10):
			cnt += helper(n, i)
		return cnt % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		d = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		cache = {}

		def dfs(l, m):
			nonlocal d
			nonlocal cache
			key = (l, m)
			if key in cache:
				return cache[key]
			if m == n:
				return 1
			ans = 0
			for v in d[l]:
				ans += dfs(v, m + 1)
			cache[key] = ans
			return ans
		ret = 0
		for i in range(10):
			ret += dfs(i, 1)
		return ret % (10 ** 9 + 7)


class Solution:

	def __init__(self):
		self.paths = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

	def knightDialer(self, n: int) -> int:
		cache = {}

		def ways(number, turns):
			if turns < 2:
				return turns
			key = (number, turns)
			if key in cache:
				return cache[key]
			total_ways = 0
			for new_number in self.paths[number]:
				total_ways += ways(new_number, turns - 1)
			cache[key] = total_ways
			return cache[key]
		total_ways = 0
		for i in range(10):
			total_ways += ways(i, n)
		return total_ways % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {0: (4, 6), 1: (8, 6), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}

		@lru_cache(None)
		def dfs(last_val=None, length=0):
			if length == n:
				return 1
			count = 0
			if not length:
				for i in range(0, 10):
					count += dfs(i, 1)
			elif last_val != 5:
				for i in moves[last_val]:
					count += dfs(i, length + 1)
			return count
		return dfs() % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		dp = [[0] * 10 for _ in range(n)]
		for i in range(10):
			dp[0][i] = 1
		for i_n in range(0, n - 1):
			for i in range(10):
				for nei in moves[i]:
					dp[i_n + 1][nei] += dp[i_n][i]
					dp[i_n + 1][nei] %= MOD
		res = 0
		for i in range(10):
			res += dp[n - 1][i]
			res %= MOD
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		MOD = 10 ** 9 + 7
		res = 0
		cache = {}
		for i in range(10):
			res += self.helper(i, n, neighbors, cache)
		return res % MOD

	def helper(self, num, hops, neighbors, cache):
		if hops == 1:
			return 1
		if (num, hops) in cache:
			return cache[num, hops]
		seq = 0
		for i in neighbors[num]:
			seq += self.helper(i, hops - 1, neighbors, cache)
		cache[num, hops] = seq
		return seq


class Solution:

	def knightDialer(self, n: int) -> int:
		modulo = 10 ** 9 + 7
		dp = [1] * 10
		while n > 1:
			new_table = [0] * 10
			for digit in range(0, 10):
				for neighbor in self.neighbors(digit):
					new_table[neighbor] += dp[digit]
			n -= 1
			dp = new_table
		return sum(dp) % modulo

	def neighbors(self, digit):
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		return neighbors[digit]


jumps = [(4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4)]

class Solution:

	@staticmethod
	def numNumbersFrom(cache, button, ttl):
		if ttl == 0:
			return 0
		if ttl == 1:
			return 1
		if button in cache and ttl in cache[button]:
			return cache[button][ttl]
		total = 0
		for i in jumps[button]:
			total += int(Solution.numNumbersFrom(cache, i, ttl - 1) % (1000000000.0 + 7))
		if button not in cache:
			cache[button] = {}
		cache[button][ttl] = total
		return total

	def knightDialer(self, n: int) -> int:
		total = 0
		cache = {}
		for i in range(0, len(jumps)):
			total += self.numNumbersFrom(cache, i, n)
		return int(total % (1000000000.0 + 7))


class Solution:

	def __init__(self):
		self.moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [7, 1, 0], [6, 2], [1, 3], [4, 2]]
		self.memoized_moves = {}

	def knightDialer(self, n: int) -> int:
		moves = 0
		for i in range(10):
			moves += self.calculateMoves(n - 1, i)
		return moves % (pow(10, 9) + 7)

	def calculateMoves(self, moves_remaining, current_number):
		if moves_remaining == 0:
			return 1
		moves = 0
		for next_number in self.getMoves(current_number):
			if (moves_remaining, next_number) not in self.memoized_moves:
				self.memoized_moves[moves_remaining, next_number] = self.calculateMoves(moves_remaining - 1, next_number)
			moves += self.memoized_moves[moves_remaining, next_number]
		return moves

	def getMoves(self, number):
		return self.moves[number]


NEIGHBORS_MAP = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}

class Solution:

	def nextPositions(self, n):
		return NEIGHBORS_MAP[n]

	def build_x_y_map(self):
		(r, c) = (0, 0)
		ht = {}
		for i in range(1, 10):
			ht[i] = (r, c)
			c += 1
			if c == 3:
				r += 1
				c = 0
		ht[0] = (3, 1)
		return ht

	def knightDialer(self, n: int) -> int:

		def count_moves(curr_cell, hops, memo):
			if hops == 0:
				return 1
			key = (curr_cell, hops)
			if key not in memo:
				ways = 0
				for pos in self.nextPositions(curr_cell):
					ways += count_moves(pos, hops - 1, memo)
				memo[key] = ways
			return memo[key]
		total = 0
		memo = {}
		for i in range(0, 10):
			total += count_moves(i, n - 1, memo)
		return total % (10 ** 9 + 7)


class Solution:

	def nextHops(self, row: int, col: int) -> list:
		hops = []
		if (row, col) not in self.hopDict:
			for jump in [(-2, -1), (-1, -2), (1, -2), (2, -1), (2, 1), (1, 2), (-1, 2), (-2, 1)]:
				(nr, nc) = (row + jump[0], col + jump[1])
				if nr < 0 or nc < 0 or nr > 2 or (nc > 2):
					if nr == 3 and nc == 1:
						hops.append((nr, nc))
					continue
				hops.append((nr, nc))
			self.hopDict[row, col] = hops
		return self.hopDict[row, col]

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return
		reached = [[1] * 3 for _ in range(4)]
		reached[3][0] = 0
		reached[3][2] = 0
		self.hopDict = {}
		for move in range(2, n + 1):
			nreached = [[0] * 3 for _ in range(4)]
			for (i, row) in enumerate(reached):
				for (j, button) in enumerate(row):
					if button == 0:
						continue
					for hop in self.nextHops(i, j):
						nreached[hop[0]][hop[1]] += button
						nreached[hop[0]][hop[1]] %= 10 ** 9 + 7
			reached = nreached
		return sum(map(sum, reached)) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		maxs = 10 ** 9 + 7
		moves = ((-1, -2), (-2, -1), (-2, 1), (-1, 2), (1, 2), (2, 1), (2, -1), (1, -2))
		memo = {}
		neighbors = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}

		def dfs(i, n):
			if n == 1:
				return 1
			if (n, i) in memo:
				return memo[n, i]
			else:
				nums = 0
				for d in neighbors[i]:
					nums += dfs(d, n - 1)
				memo[n, i] = nums
			return nums
		total = 0
		for i in range(10):
			total += dfs(i, N)
		return total % maxs


move_map = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 0, 7}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

class Solution:

	def dfs(self, n, key):
		if n == 1:
			return 1
		if (n, key) in self.memo:
			return self.memo[n, key]
		res = 0
		for new_key in move_map[key]:
			res += self.dfs(n - 1, new_key)
		self.memo[n, key] = res
		return res

	def knightDialer(self, n: int) -> int:
		self.memo = {}
		res = 0
		for key in move_map:
			res += self.dfs(n, key)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		jump_map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp_map = {}

		def get_num(s, n):
			if (s, n) not in dp_map:
				if n == 1:
					dp_map[s, n] = 1
					return dp_map[s, n]
				ans = 0
				for target in jump_map[s]:
					ans += get_num(target, n - 1)
				dp_map[s, n] = ans
			return dp_map[s, n]
		total = 0
		for i in jump_map.keys():
			total += get_num(i, N)
		return total % (10 ** 9 + 7)


class Solution:

	def _knightDialer(self, n: int, curr_n: int, moves_map: dict, cache: dict) -> int:
		if n == 0:
			return 1
		if (curr_n, n) in cache:
			return cache[curr_n, n]
		distinct_nums = 0
		for next_n in moves_map[curr_n]:
			distinct_nums += self._knightDialer(n - 1, next_n, moves_map, cache)
		cache[curr_n, n] = distinct_nums
		return cache[curr_n, n]

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		mod = 10 ** 9 + 7
		nums = 0
		cache = {}
		moves_map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		nums = 0
		for (m, weight) in [(1, 4), (2, 2), (4, 2), (0, 1)]:
			nums += weight * self._knightDialer(n - 1, m, moves_map, cache)
		return nums % mod


class Solution:

	def helper(self, keys, n, digit, cache):
		if not n:
			return 1
		if (n, digit) in cache:
			return cache[n, digit]
		count = 0
		for d in keys[digit]:
			count += self.helper(keys, n - 1, d, cache)
		cache[n, digit] = count
		return cache[n, digit]

	def knightDialer(self, n: int) -> int:
		keys = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [7, 1, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		count = 0
		cache = {}
		for i in range(0, 10):
			count += self.helper(keys, n - 1, i, cache)
		return count % (10 ** 9 + 7)


from functools import lru_cache

class Solution:

	def knightDialer(self, n: int) -> int:
		neighbors = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		@lru_cache(None)
		def dfs(i, n):
			if n == 1:
				return 1
			count = 0
			for x in neighbors[i]:
				count = (count + dfs(x, n - 1)) % (10 ** 9 + 7)
			return count
		ansr = 0
		for i in range(10):
			ansr = (ansr + dfs(i, n)) % (10 ** 9 + 7)
		return ansr


MOVES = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]

class Solution:

	def knightDialer(self, N: int) -> int:
		memo = {}
		res = 0
		for i in range(10):
			res += self._dfs(i, N, memo)
		return res % (10 ** 9 + 7)

	def _dfs(self, curr, steps, memo):
		if steps == 1:
			return 1
		key = (curr, steps)
		if key in memo:
			return memo[key]
		memo[key] = 0
		for next_digit in MOVES[curr]:
			memo[key] += self._dfs(next_digit, steps - 1, memo)
		return memo[key]


class Solution:

	def knightDialer(self, n: int) -> int:
		dic = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		MOD = 10 ** 9 + 7
		cache = {}

		def dfs(start, digit):
			key = (start, digit)
			if key in cache:
				return cache[key]
			if digit == 0:
				return 1
			if digit < 0:
				return 0
			ans = 0
			if dic.get(start, -1) == -1:
				return 0
			for neigh in dic[start]:
				ans += dfs(neigh, digit - 1)
			cache[key] = ans
			return ans
		count = 0
		for i in range(10):
			count = (count + dfs(i, n - 1)) % MOD
		return count


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		M = [[0 for i in range(10)] for j in range(n + 1)]
		next_move = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def paths(pos, nhop):
			if nhop == 1:
				return 1
			if M[nhop][pos] > 0:
				return M[nhop][pos]
			for j in range(len(next_move[pos])):
				M[nhop][pos] += paths(next_move[pos][j], nhop - 1) % MOD
			return M[nhop][pos]
		ans = 0
		for start in range(10):
			ans = (ans + paths(start, n)) % MOD
		return int(ans)


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		if n == 1:
			return 10
		dic = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: {1, 7, 0}, 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		memo = {}

		def dfs(cur, n):
			if n == 0:
				return 1
			if (cur, n) in memo:
				return memo[cur, n]
			ret = 0
			for nxt in dic.get(cur, []):
				ret += dfs(nxt, n - 1)
			memo[cur, n] = ret
			return ret
		ret = 0
		for i in range(10):
			ret += dfs(i, n - 1)
			ret %= mod
		return ret


class Solution:

	def dfs(self, i, N):
		if N == 1:
			return 1
		if (i, N) in self.memo:
			return self.memo[i, N]
		ans = 0
		for nxt in self.map[i]:
			ans += self.dfs(nxt, N - 1)
		self.memo[i, N] = ans
		return ans

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		if n == 1:
			return 10
		self.map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		self.memo = {}
		ans = 0
		for i in range(10):
			if i == 5:
				continue
			ans = (ans + self.dfs(i, n)) % (10 ** 9 + 7)
		return ans


class Solution:
	NEIGHBORS = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: (), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4)}

	def numsFromPos(self, num, jumps):
		jumps_remaining = jumps - 1
		if not jumps_remaining:
			return 1
		if (num, jumps) in self.cache:
			return self.cache[num, jumps]
		res = 0
		for nei in self.NEIGHBORS[num]:
			res += self.numsFromPos(nei, jumps_remaining)
		self.cache[num, jumps] = res
		return res

	def knightDialer(self, n: int) -> int:
		self.cache = {}
		res = 0
		for i in range(10):
			res += self.numsFromPos(i, n)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		x1 = x2 = x3 = x4 = x5 = x6 = x7 = x8 = x9 = x0 = 1
		for _ in range(N - 1):
			(x1, x2, x3, x4, x5, x6, x7, x8, x9, x0) = (x8 + x6, x7 + x9, x4 + x8, x3 + x9 + x0, 0, x1 + x7 + x0, x2 + x6, x1 + x3, x2 + x4, x4 + x6)
		return (x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x0) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: 'int') -> 'int':
		path_graph = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		mem = {}
		if N == 1:
			return 10

		def dfs(n, steps):
			if steps == 1:
				return len(path_graph[n])
			if (n, steps) not in mem:
				all_paths = 0
				for next_num in path_graph[n]:
					all_paths += dfs(next_num, steps - 1)
				mem[n, steps] = all_paths
			return mem[n, steps]
		result = 0
		for n in range(10):
			temp = dfs(n, N - 1)
			result += temp
		return result % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:

		def dfs(pos, remain):
			if remain == 0:
				return 1
			if not (pos, remain) in memo:
				cur = 0
				for np in pos_map[pos]:
					cur += dfs(np, remain - 1)
				memo[pos, remain] = cur
			return memo[pos, remain]
		res = 0
		memo = {}
		pos_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		for i in range(10):
			res += dfs(i, n - 1)
		return res % (pow(10, 9) + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		self.mod_Val = 10 ** 9 + 7
		self.map = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		self.ans = 0
		self.mem = collections.defaultdict(int)
		for i in range(10):
			self.ans += self.recursion(n - 1, i)
		return self.ans % self.mod_Val

	def recursion(self, hops, s):
		if not hops:
			return 1
		count = 0
		if (hops, s) not in self.mem:
			for n in self.map[s]:
				count += self.recursion(hops - 1, n)
			self.mem[hops, s] = count
		return self.mem[hops, s]


class Solution:

	def knightDialer(self, n: int) -> int:
		mem = [[1] for i in range(10)]
		for i in range(1, n):
			for cell in range(10):
				mem[cell].append(self.knightDialerHelper(i, cell, mem))
		ans = sum([x[n - 1] for x in mem])
		return ans % (10 ** 9 + 7)

	def knightDialerHelper(self, n, cellNumber, mem):
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		ans = 0
		for nextCell in moves[cellNumber]:
			ans += mem[nextCell][n - 1]
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		dp = [[0 for j in range(10)] for i in range(n)]
		for i in range(10):
			dp[0][i] = 1
		for i in range(1, n):
			for j in range(10):
				for nei in moves[j]:
					dp[i][nei] += dp[i - 1][j]
					dp[i][nei] = dp[i][nei] % mod
		res = sum(dp[n - 1]) % mod
		return res


class Solution:

	def knightDialer(self, N: int) -> int:
		solution = 0
		self.valid_jumps = {1: [6, 8], 2: [9, 7], 3: [8, 4], 4: [9, 3, 0], 5: [], 6: [7, 1, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}
		self.N = N
		self.cache = {}
		solution = 0
		for i in range(10):
			solution += self.jump_around(1, i)
		return solution % (pow(10, 9) + 7)

	def jump_around(self, number_len_so_far, last_number):
		if (number_len_so_far, last_number) in self.cache:
			return self.cache[number_len_so_far, last_number]
		if number_len_so_far == self.N:
			return 1
		else:
			solution_for_this_set = 0
			possible_jumps = self.valid_jumps[last_number]
			for possible_jump in possible_jumps:
				solution_for_this_set += self.jump_around(number_len_so_far + 1, possible_jump)
			self.cache[number_len_so_far, last_number] = solution_for_this_set
			return solution_for_this_set


class Solution:

	def knightDialer(self, n: int) -> int:
		next_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = {}

		def dfs(cur_num, n):
			if (cur_num, n) in memo.keys():
				return memo[cur_num, n]
			if n == 0:
				return 1
			ans = 0
			for next_num in next_map[cur_num]:
				ans += dfs(next_num, n - 1)
			memo[cur_num, n] = ans
			return ans
		ans = 0
		MOD = pow(10, 9) + 7
		memo = {}
		for i in range(10):
			ans += dfs(i, n - 1) % MOD
			ans = ans % MOD
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		M = 10 ** 9 + 7
		current_ways = [1] * 10
		for i in range(1, n):
			prev = current_ways.copy()
			current_ways[0] = (prev[4] + prev[6]) % M
			current_ways[1] = (prev[6] + prev[8]) % M
			current_ways[2] = (prev[7] + prev[9]) % M
			current_ways[3] = (prev[4] + prev[8]) % M
			current_ways[4] = (prev[3] + prev[9] + prev[0]) % M
			current_ways[5] = 0
			current_ways[6] = (prev[1] + prev[7] + prev[0]) % M
			current_ways[7] = (prev[2] + prev[6]) % M
			current_ways[8] = (prev[1] + prev[3]) % M
			current_ways[9] = (prev[2] + prev[4]) % M
		return sum(current_ways) % M


class Solution:

	def knightDialer(self, n: int) -> int:
		memo = {}
		pos = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [3, 1], 9: [2, 4], 0: [6, 4]}
		res = 0
		mod = 10 ** 9 + 7

		def recur(i, hops):
			if (i, hops) in memo:
				return memo[i, hops]
			if hops == 0:
				return 1
			cnt = 0
			for nums in pos[i]:
				cnt += recur(nums, hops - 1)
				memo[i, hops] = cnt
			return cnt
		for i in range(10):
			res += recur(i, n - 1)
		return res % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		nbrs = {1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		self.memo = {}

		def find_count(idx, num):
			if idx == n:
				return 1
			if (num, idx) in self.memo:
				return self.memo[num, idx]
			count = 0
			for nbr in nbrs[num]:
				count += find_count(idx + 1, nbr)
			self.memo[num, idx] = count
			return count
		ans = 0
		for i in range(10):
			ans += find_count(1, i)
		mod = 10 ** 9 + 7
		return ans % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [0 for i in range(12)]
		num = [1, 2, 3, 4, 5, 6, 7, 8, 9, 11]
		for j in num:
			dp[j] = 1
		for i in range(1, n):
			temp = [0 for l in range(12)]
			for j in num:
				if j % 3 == 0:
					temp[j] += dp[j + 5] if j + 5 in num else 0
					temp[j] += dp[j - 5] if j - 5 in num else 0
					temp[j] += dp[j + 1] if j + 1 in num else 0
					temp[j] += dp[j - 7] if j - 7 in num else 0
				elif j % 3 == 1:
					temp[j] += dp[j + 5] if j + 5 in num else 0
					temp[j] += dp[j - 5] if j - 5 in num else 0
					temp[j] += dp[j + 7] if j + 7 in num else 0
					temp[j] += dp[j - 1] if j - 1 in num else 0
				else:
					temp[j] += dp[j + 5] if j + 5 in num else 0
					temp[j] += dp[j - 5] if j - 5 in num else 0
					temp[j] += dp[j + 7] if j + 7 in num else 0
					temp[j] += dp[j - 7] if j - 7 in num else 0
			dp = temp
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def __init__(self):
		self.moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [7, 1, 0], [6, 2], [1, 3], [4, 2]]
		self.memoized_numbers = {}

	def knightDialer(self, n: int) -> int:
		distinctPhoneNumbers = 0
		for i in range(10):
			distinctPhoneNumbers += self.getPhoneNumbers(n - 1, i)
		return distinctPhoneNumbers % (pow(10, 9) + 7)

	def getPhoneNumbers(self, moves_remaining, current_number):
		if moves_remaining == 0:
			return 1
		else:
			moves = 0
			for number in self.getMoves(current_number):
				if (moves_remaining, number) not in list(self.memoized_numbers.keys()):
					self.memoized_numbers[moves_remaining, number] = self.getPhoneNumbers(moves_remaining - 1, number)
				moves += self.memoized_numbers[moves_remaining, number]
			return moves

	def getMoves(self, move):
		return self.moves[move]


from collections import defaultdict

class Solution:

	def knightDialer(self, N: int) -> int:
		MOD = 10 ** 9 + 7
		board = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [-1, 0, -1]]
		dp = defaultdict(int)
		movesC = {}

		def moves(i, j):
			valids = set()
			for (u, v) in [(i - 1, j + 2), (i + 1, j + 2), (i - 1, j - 2), (i + 1, j - 2), (i - 2, j + 1), (i - 2, j - 1), (i + 2, j + 1), (i + 2, j - 1)]:
				if u < 0 or v < 0 or u >= len(board) or (v >= 3):
					continue
				if board[u][v] != -1:
					valids.add((u, v))
			return valids
		for i in range(len(board)):
			for j in range(3):
				if board[i][j] != -1:
					movesC[i, j] = moves(i, j)
		total = 0
		for n in range(1, N + 1):
			for i in range(len(board)):
				for j in range(len(board[i])):
					num = board[i][j]
					if num != -1:
						key = (i, j, n)
						if n == 1:
							dp[key] = 1
						else:
							for (u, v) in movesC[i, j]:
								dp[key] += dp[u, v, n - 1] % MOD
						if n == N:
							total += dp[key] % MOD
		return total % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		MOD = 10 ** 9 + 7
		poss = {}
		poss[1] = [6, 8]
		poss[2] = [7, 9]
		poss[3] = [4, 8]
		poss[4] = [3, 9, 0]
		poss[5] = []
		poss[6] = [1, 7, 0]
		poss[7] = [2, 6]
		poss[8] = [1, 3]
		poss[9] = [2, 4]
		poss[0] = [4, 6]

		def helper(numb, i):
			if i == n:
				return 1
			if (numb, i) in mem:
				return mem[numb, i]
			out = 0
			child = poss[numb]
			nchild = len(child)
			for j in range(nchild):
				val = child[j]
				out += helper(val, i + 1)
				out = out % MOD
			mem[numb, i] = out
			return out
		res = 0
		mem = {}
		for i in range(10):
			res += helper(i, 1)
		return res % MOD


from collections import deque

class Solution:

	def __init__(self):
		self.next_move = [(4, 6), (6, 8), (7, 9), (4, 8), (3, 0, 9), (), (1, 7, 0), (6, 2), (3, 1), (2, 4)]
		self.cache = {}

	def dfs(self, start, n):
		if n == 0:
			return 1
		if not self.cache.get((start, n)):
			total_numbers = 0
			for i in self.next_move[start]:
				total_numbers += self.dfs(i, n - 1)
			self.cache[start, n] = total_numbers
		return self.cache[start, n]

	def knightDialer(self, n: int) -> int:
		return sum([self.dfs(i, n - 1) for i in range(10)]) % (10 ** 9 + 7)


class Solution:

	def __init__(self):
		self.moves = [[4, 6], [8, 6], [7, 9], [4, 8], [9, 3, 0], [], [7, 1, 0], [6, 2], [1, 3], [2, 4]]
		self.memoized_current_number_and_remaining_moves = {}

	def getNextMoves(self, current_number):
		return self.moves[current_number]

	def knightDialer(self, n: int) -> int:
		total_moves = 0
		for number in range(10):
			total_moves += self.knightDialerOneNumber(number, n - 1)
		return total_moves % (pow(10, 9) + 7)

	def knightDialerOneNumber(self, current_number, moves_left):
		if moves_left == 0:
			return 1
		moves = 0
		for move in self.getNextMoves(current_number):
			if (move, moves_left) in list(self.memoized_current_number_and_remaining_moves.keys()):
				moves += self.memoized_current_number_and_remaining_moves[move, moves_left]
			else:
				self.memoized_current_number_and_remaining_moves[move, moves_left] = self.knightDialerOneNumber(move, moves_left - 1)
				moves += self.memoized_current_number_and_remaining_moves[move, moves_left]
		return moves


class Solution:
	valid_jumps = dict()
	valid_jumps[0] = [4, 6]
	valid_jumps[1] = [6, 8]
	valid_jumps[2] = [7, 9]
	valid_jumps[3] = [4, 8]
	valid_jumps[4] = [0, 3, 9]
	valid_jumps[5] = []
	valid_jumps[6] = [0, 1, 7]
	valid_jumps[7] = [2, 6]
	valid_jumps[8] = [1, 3]
	valid_jumps[9] = [2, 4]
	cache = dict()

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		agg = 0
		for idx in range(10):
			if idx != 5:
				agg += self.knightDialerHelper(idx, n - 1)
		return agg % int(1000000000.0 + 7)

	def knightDialerHelper(self, start, n):
		if n == 1:
			return len(self.valid_jumps[start])
		if (start, n) in self.cache.keys():
			return self.cache[start, n]
		numbers = 0
		for k in self.valid_jumps[start]:
			numbers += self.knightDialerHelper(k, n - 1)
		self.cache[start, n] = numbers
		return numbers


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1 for x in range(10)]
		for index in range(n - 1):
			newDp = [dp[4] + dp[6], dp[6] + dp[8], dp[7] + dp[9], dp[8] + dp[4], dp[9] + dp[3] + dp[0], 0, dp[1] + dp[7] + dp[0], dp[2] + dp[6], dp[1] + dp[3], dp[4] + dp[2]]
			dp = newDp
		return sum(dp) % (10 ** 9 + 7)


from collections import defaultdict

class Solution:

	def knightDialer(self, n: int) -> int:
		G = {1: [6, 8], 2: [7, 9], 3: [4, 8], 6: [1, 7, 0], 5: [], 4: [3, 9, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = defaultdict(lambda : defaultdict(lambda : 0))

		def dfs(number, numberOfMovements):
			if numberOfMovements == 0:
				return 1
			if dp[number][numberOfMovements]:
				return dp[number][numberOfMovements]
			total = 0
			for i in G[number]:
				total += dfs(i, numberOfMovements - 1)
			dp[number][numberOfMovements] = total
			return total
		res = 0
		for i in range(10):
			res += dfs(i, n - 1)
			res = res % 1000000007
		return res


import numpy as np

class Solution:

	def knightDialer(self, n: int) -> int:
		ans = np.ones((10,), dtype=int)
		table = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [4, 2]}
		for i in range(n - 1):
			tempans = np.zeros((10,), dtype=int)
			for j in range(10):
				if j != 5:
					values = table.get(j)
					for value in values:
						tempans[value] += ans[j]
			ans = tempans
			if sum(ans) > 10 ** 9 + 7:
				ans = ans % (10 ** 9 + 7)
		return sum(ans) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		if n <= 0:
			return 0
		MOD = 10 ** 9 + 7
		g = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		dp = [[None] * 10 for _ in range(n + 1)]

		def kd(n, start):
			if n == 1:
				return 1
			if dp[n][start] is None:
				dp[n][start] = sum([kd(n - 1, nxt) for nxt in g[start]])
			return dp[n][start]
		return sum((kd(n, start) for start in range(10))) % MOD


class Solution:

	def knightDialer(self, N: int) -> int:
		g = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [4, 2]}
		A = [[1 if i in g[j] else 0 for i in range(10)] for j in range(10)]
		v = [1] * 10
		for _ in range(N - 1):
			res = [0] * 10
			for r in range(10):
				for c in range(10):
					if A[r][c]:
						res[c] += v[r]
			v = res
		return sum(v) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		adj = {1: [6, 8], 2: [7, 9], 3: [8, 4], 4: [0, 9, 3], 5: [], 6: [7, 1, 0], 7: [6, 2], 8: [3, 1], 9: [4, 2], 0: [6, 4]}
		res = 0
		memo = collections.defaultdict(int)
		for i in range(10):
			res = (res + self.top_down(memo, adj, n - 1, i)) % (10 ** 9 + 7)
		return res

	def top_down(self, memo, adj, n, cur):
		if n == 0:
			return 1
		if (cur, n) not in memo:
			for nb in adj[cur]:
				memo[cur, n] += self.top_down(memo, adj, n - 1, nb) % (10 ** 9 + 7)
		return memo[cur, n]


class Solution:

	def pos(self, idx):
		return {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [4, 2]}[idx]

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		memo = [[0 for _ in range(n + 1)] for i in range(10)]
		for i in range(10):
			memo[i][1] = 1
		for s in range(2, n + 1):
			for idx in range(10):
				for p in self.pos(idx):
					memo[idx][s] += memo[p][s - 1]
		return sum((memo[i][n] for i in range(10))) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		jumps = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
		mod = 10 ** 9 + 7
		memo = {}

		def helper(n, starting, memo):
			if (n, starting) in memo:
				return memo[n, starting]
			if n == 1:
				return 1
			if n == 2:
				return len(jumps[starting])
			sum = 0
			for jump_location in jumps[starting]:
				sum += helper(n - 1, jump_location, memo)
			memo[n, starting] = sum
			return sum
		total_jumps = 0
		for i in range(10):
			if i == 5 and n != 1:
				continue
			total_jumps += helper(n, i, memo)
		return total_jumps % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		path = [(4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4)]
		memo = []
		for i in range(n + 1):
			memo.append({})
			for j in range(10):
				memo[i][j] = -1

		def dp(num, steps):
			if steps == 1:
				return 1
			if memo[steps][num] != -1:
				return memo[steps][num]
			ret = 0
			for i in path[num]:
				ret += dp(i, steps - 1)
			memo[steps][num] = ret
			return ret % 1000000007
		res = 0
		for num in range(10):
			res += dp(num, n)
			res %= 1000000007
		return res


import numpy as np

class Solution:

	def knightDialer(self, N: int) -> int:
		goto = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = np.zeros((10, N)).astype(int)
		dp[:, 0] = 1
		for c in range(1, N):
			for p in range(10):
				for next_vals in goto[p]:
					dp[p, c] += dp[next_vals, c - 1] % (10 ** 9 + 7)
		return int(sum(dp[:, N - 1])) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		myMap = {1: [8, 6], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6], -1: list(range(10))}
		cache = {}

		def dfs(start, level):
			if level == 0:
				return 1
			key = str(start) + str(level)
			if key in cache:
				return cache[key]
			else:
				ans = 0
				for number in myMap[start]:
					ans += dfs(number, level - 1)
				cache[key] = ans
				return ans
		total = dfs(-1, N)
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		NEIGHBORS_MAP = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		mx = 10 ** 9 + 7
		memo = {}

		def dp(n, curr_num):
			if (n, curr_num) in memo:
				return memo[n, curr_num]
			if n == N - 1:
				return 1
			comb = 0
			for neighbor in NEIGHBORS_MAP[curr_num]:
				comb += dp(n + 1, neighbor)
			memo[n, curr_num] = comb
			return comb
		res = 0
		for i in range(0, 10):
			res += dp(0, i)
		return res % mx


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		c = [1] * 10
		for _ in range(n - 1):
			c = [c[4] + c[6], c[6] + c[8], c[7] + c[9], c[4] + c[8], c[0] + c[3] + c[9], 0, c[0] + c[7] + c[1], c[2] + c[6], c[1] + c[3], c[2] + c[4]]
		return sum(c) % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		next = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}
		M = 1000000007
		cache = defaultdict(int)

		def helper(m, n):
			if (m, n) not in cache:
				if n == 1:
					cache[m, n] = 1
				else:
					for nn in next[m]:
						cache[m, n] += helper(nn, n - 1)
				cache[m, n] %= M
			return cache[m, n]
		return sum((helper(i, n) for i in range(10))) % M


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		hash_map = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		dp = {}

		def ways_n(n, val):
			if n == 0:
				return 1
			if (n, val) in dp:
				return dp[n, val]
			dp[n, val] = 0
			for i in hash_map[val]:
				dp[n, val] += ways_n(n - 1, i)
			return dp[n, val]
		ans = 0
		for i in range(10):
			ans += ways_n(n - 1, i)
		return ans % (10 ** 9 + 7)


class Solution:

	def getAccessible(self, key):
		switch = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		return switch.setdefault(key, [])

	def knightDialer(self, n: int) -> int:
		dp = [[0] * 10 for _ in range(n)]
		dp[0] = [1] * 10
		for r in range(1, len(dp)):
			for c in range(len(dp[0])):
				neighbors = self.getAccessible(c)
				for n in neighbors:
					dp[r][c] = dp[r - 1][n] + dp[r][c] % (10 ** 9 + 7)
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		possible_ways = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		remember_dict = {}

		def numofways(N, startnum):
			if (startnum, N) in remember_dict:
				return remember_dict[startnum, N]
			if N == 1:
				return 1
			else:
				temp = 0
				for nextnum in possible_ways[startnum]:
					temp += numofways(N - 1, nextnum)
				remember_dict[startnum, N] = temp
				return temp
		summation = 0
		for i in range(10):
			summation += numofways(N, i)
		return summation % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		cache = [[0 for i in range(n + 1)] for i in range(10)]
		for i in range(10):
			cache[i][1] = 1
		return self.hopper(n, cache) % (10 ** 9 + 7)

	def hopper(self, hops_left, cache):
		if hops_left == 1:
			return sum([cache[i][1] for i in range(10)])
		elif hops_left < 1:
			return 0
		else:
			for i in range(2, hops_left + 1):
				for j in range(10):
					for nbr in self.nbrs(j):
						cache[j][i] += cache[nbr][i - 1]
		return sum([cache[i][hops_left] for i in range(10)])

	def nbrs(self, ind):
		nbrs = {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [4, 2]}
		return nbrs[ind]


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {0: [4, 6], 2: [7, 9], 1: [6, 8], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		store = {}

		def f(num, rem):
			if rem == 1:
				return 1
			if (num, rem) in store:
				return store[num, rem]
			res = store[num, rem] = sum([f(m, rem - 1) for m in moves[num]])
			return res
		return sum([f(num, n) for num in range(10)]) % (10 ** 9 + 7)


class Solution:
	arr = None

	def knightDialer(self, n: int) -> int:
		self.init_arr(n)
		if n == 1:
			return 10
		total = 0
		for j in range(2, n + 1):
			for i in range(10):
				self.dialStart(i, j)
		return self.get_ans(n)

	def get_ans(self, n):
		total = 0
		for i in range(10):
			total = (total + self.arr[i][n]) % 1000000007
		return total

	def init_arr(self, n):
		self.arr = [[0] * (n + 1) for i in range(10)]
		for i in range(10):
			self.arr[i][1] = 1

	def dialStart(self, start: int, n: int):
		neighbours = self.get_neighbours()
		total = 0
		for ne in neighbours[start]:
			total = (total + self.arr[ne][n - 1]) % 1000000007
		self.arr[start][n] = total

	def get_neighbours(self):
		return {0: [4, 6], 1: [8, 6], 2: [7, 9], 3: [8, 4], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}


class Solution:

	def knightDialer(self, n: int) -> int:
		move = [1] * 10
		for i in range(n - 1):
			new_move = [1] * 10
			(new_move[0], new_move[1]) = ((move[4] + move[6]) % (10 ** 9 + 7), (move[8] + move[6]) % (10 ** 9 + 7))
			(new_move[2], new_move[3]) = ((move[7] + move[9]) % (10 ** 9 + 7), (move[8] + move[4]) % (10 ** 9 + 7))
			(new_move[4], new_move[5]) = ((move[0] + move[3] + move[9]) % (10 ** 9 + 7), 0)
			(new_move[6], new_move[7]) = ((move[0] + move[1] + move[7]) % (10 ** 9 + 7), (move[2] + move[6]) % (10 ** 9 + 7))
			(new_move[8], new_move[9]) = ((move[1] + move[3]) % (10 ** 9 + 7), (move[2] + move[4]) % (10 ** 9 + 7))
			move = new_move
		return sum(move) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 1:
			return 10
		navigation = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		memo = {}

		def get_num_distinct_dials(last_digit, N_left):
			if N_left == 0:
				return 1
			memo_key = (last_digit, N_left)
			if memo_key in memo:
				return memo[memo_key]
			result = sum([get_num_distinct_dials(next_digit, N_left - 1) for next_digit in navigation[last_digit]])
			memo[memo_key] = result
			return result
		return sum([get_num_distinct_dials(first_digit, N - 1) for first_digit in navigation.keys()]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp1 = [1] * 10
		for i in range(n - 1):
			dp2 = [0] * 10
			for digit in range(10):
				for neib in moves[digit]:
					dp2[digit] += dp1[neib]
					dp2[digit] %= pow(10, 9) + 7
			dp1 = dp2
		return sum(dp1) % (pow(10, 9) + 7)


MAX = 10 ** 9 + 7
d = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4], [4, 6]]

class Solution:

	def __init__(self):
		self.memo = {}

	def knightDialer(self, n: int) -> int:
		return sum([self.helper(n, p) for p in range(10)]) % MAX

	def helper(self, n: int, p: int) -> int:
		if (n, p) in self.memo:
			return self.memo[n, p]
		if n == 1:
			return 1
		r = sum([self.helper(n - 1, q) for q in d[p]])
		self.memo[n, p] = r
		return r


class Solution:

	def knightDialer(self, n: int) -> int:
		graph = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 9, 3], 5: [], 6: [0, 7, 1], 7: [2, 6], 8: [1, 3], 9: [4, 2]}
		ans = 0
		self.cache = {}
		for u in graph.keys():
			ans += self.dial(graph, u, n - 1)
		return ans % (10 ** 9 + 7)

	def dial(self, graph, start, n):
		if n == 0:
			return 1
		ans = 0
		key = str(start) + ' ' + str(n)
		if key in self.cache.keys():
			return self.cache[key]
		for v in graph[start]:
			ans += self.dial(graph, v, n - 1)
		self.cache[key] = ans
		return self.cache[key]


class Solution:

	def knightDialer(self, n: int) -> int:
		mod_num = 10 ** 9 + 7
		moves = [(-2, -1), (-1, -2), (1, -2), (2, -1), (-2, 1), (-1, 2), (1, 2), (2, 1)]
		cells = [(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 1)]
		cell2idx = {}
		for (i, cell) in enumerate(cells):
			cell2idx[cell] = i
		sequences = [1 for _ in cells]
		for step in range(n - 1):
			new_sequences = [0 for _ in cells]
			for (i, (r, c)) in enumerate(cells):
				for (rm, cm) in moves:
					newr = r + rm
					newc = c + cm
					if (newr, newc) in cell2idx:
						new_idx = cell2idx[newr, newc]
						new_sequences[new_idx] += sequences[i]
			sequences = [cnt % mod_num for cnt in new_sequences]
		return sum(sequences) % mod_num


class Solution:

	def knightDialer(self, N: int) -> int:
		choices = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		self.memo = dict()

		def dfs(curr, n):
			key = (curr, n)
			if key in self.memo:
				return self.memo[key]
			if n == 1:
				return 1
			sub = 0
			for next in choices[curr]:
				sub += dfs(next, n - 1)
			self.memo[key] = sub
			return sub
		res = 0
		for s in range(10):
			res += dfs(s, N)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		space = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 7, 1], 7: [2, 6], 8: [1, 3], 9: [4, 2], 0: [4, 6]}
		memory = {}
		if n < 1:
			return 0

		def recurse(number, n):
			if n < 2:
				return 1
			key = str([number, n])
			if key in memory:
				return memory[key]
			moves = 0
			for i in space[number]:
				moves += recurse(i, n - 1)
			memory[key] = moves
			return moves
		s = 0
		for number in space:
			s += recurse(number, n)
		return s % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 0:
			return 0
		d = {}
		choices = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]

		def dp(k, n):
			if n == 0:
				return 1
			if n == 1:
				return len(choices[k])
			if (k, n) not in d:
				d[k, n] = sum([dp(nxt, n - 1) for nxt in choices[k]])
			return d[k, n]
		return sum([dp(v, N - 1) for v in range(10)]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		cell2jump = dict()
		cell2jump[1] = [6, 8]
		cell2jump[2] = [7, 9]
		cell2jump[3] = [4, 8]
		cell2jump[4] = [3, 9, 0]
		cell2jump[5] = []
		cell2jump[6] = [1, 7, 0]
		cell2jump[7] = [2, 6]
		cell2jump[8] = [1, 3]
		cell2jump[9] = [2, 4]
		cell2jump[0] = [4, 6]
		dp = defaultdict()

		def helper(num_jumps, cell):
			if num_jumps == 1:
				return 1
			elif num_jumps == 2:
				return len(cell2jump[cell])
			if (num_jumps, cell) in dp:
				return dp[num_jumps, cell]
			res = 0
			for nei in cell2jump[cell]:
				res += helper(num_jumps - 1, nei)
			dp[num_jumps, cell] = res
			return res
		total = []
		for i in range(10):
			total.append(helper(n, i))
		return sum(total) % (10 ** 9 + 7)


from functools import lru_cache

class Solution:

	def knightDialer(self, n: int) -> int:
		to = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}

		@lru_cache(maxsize=None)
		def dfs(i: int, k: int) -> int:
			if i not in to:
				return 0
			if k == 1:
				return 1
			return sum([dfs(t, k - 1) for t in to[i]])
		return sum([dfs(i, n) for i in range(10)]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		mod = 10 ** 9 + 7

		def getNeighbors(N):
			neighs = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
			return neighs[N]

		def getCount(start, n):
			if (start, n) not in dic:
				if n == 0:
					dic[start, n] = 1
				else:
					count = 0
					for nei in getNeighbors(start):
						count += getCount(nei, n - 1)
					dic[start, n] = count
			return dic[start, n]
		dic = {}
		val = 0
		for i in range(10):
			val += getCount(i, N - 1)
		return val % mod


from functools import lru_cache

class Solution:

	def knightDialer(self, N: int) -> int:
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]

		@lru_cache(maxsize=None)
		def dfs(s, n):
			if n == 0:
				return 1
			return sum([dfs(v, n - 1) for v in moves[s]])
		answer = 0
		for i in range(10):
			answer += dfs(i, N - 1)
			answer %= 10 ** 9 + 7
		return answer % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		parent_child_dict = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		dp = [[0] * 10 for _ in range(N)]
		for j in range(10):
			dp[0][j] = 1
		for i in range(N - 1):
			for j in range(10):
				children = parent_child_dict[j]
				for child in children:
					dp[i + 1][child] += dp[i][j]
				dp[i][j] = dp[i][j] % (10 ** 9 + 7)
		return sum(dp[N - 1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = {}

		def nextStep(k):
			if k == 1:
				return [6, 8]
			if k == 2:
				return [7, 9]
			if k == 3:
				return [4, 8]
			if k == 4:
				return [9, 3, 0]
			if k == 6:
				return [7, 1, 0]
			if k == 7:
				return [6, 2]
			if k == 8:
				return [1, 3]
			if k == 9:
				return [4, 2]
			if k == 0:
				return [4, 6]

		def dfs(k, step):
			if k == 5 and step > 1:
				return 0
			if step == 1:
				return 1
			key = (k, step)
			if key in dp:
				return dp[key]
			dp[key] = sum([dfs(e, step - 1) for e in nextStep(k)])
			return dp[key]
		res = 0
		for i in range(10):
			res += dfs(i, n)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = {i: 1 for i in range(10)}
		mod = 10 ** 9 + 7
		for _ in range(1, n):
			dp2 = {}
			dp2[0] = (dp[4] + dp[6]) % mod
			dp2[1] = (dp[6] + dp[8]) % mod
			dp2[2] = (dp[7] + dp[9]) % mod
			dp2[3] = (dp[4] + dp[8]) % mod
			dp2[4] = (dp[0] + dp[3] + dp[9]) % mod
			dp2[5] = 0
			dp2[6] = (dp[0] + dp[1] + dp[7]) % mod
			dp2[7] = (dp[2] + dp[6]) % mod
			dp2[8] = (dp[1] + dp[3]) % mod
			dp2[9] = (dp[2] + dp[4]) % mod
			dp = dp2
		return sum(dp.values()) % mod


NEIGHBORS_MAP = {1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (3, 9, 0), 5: tuple(), 6: (1, 7, 0), 7: (2, 6), 8: (1, 3), 9: (2, 4), 0: (4, 6)}

def neighbors(position):
	return NEIGHBORS_MAP[position]

class Solution:

	def knightDialer(self, num_hops):
		cache = {}
		mod = 10 ** 9 + 7

		def helper(position, num_hops):
			if (position, num_hops) in cache:
				return cache[position, num_hops]
			if num_hops == 0 or num_hops == 1:
				return 1
			num_sequences = 0
			for neighbor in neighbors(position):
				num_sequences += helper(neighbor, num_hops - 1)
			cache[position, num_hops] = num_sequences
			return num_sequences
		res = 0
		for i in range(0, 10):
			res += helper(i, num_hops)
		return res % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		Mod = 10 ** 9 + 7
		dirs = [(-2, -1), (-2, 1), (-1, -2), (-1, 2), (1, -2), (1, 2), (2, -1), (2, 1)]
		dp = [[1] * 3 for _ in range(4)]
		dp[3][0] = 0
		dp[3][2] = 0
		for k in range(1, n):
			temp = [[0] * 3 for _ in range(4)]
			for i in range(4):
				for j in range(3):
					if i == 3 and j != 1:
						continue
					for (x, y) in dirs:
						nx = i + x
						ny = j + y
						if nx < 0 or nx >= 4 or ny < 0 or (ny >= 3):
							continue
						temp[i][j] = (temp[i][j] + dp[nx][ny]) % Mod
			dp = temp[:]
		print(dp)
		ans = 0
		for i in range(4):
			for j in range(3):
				ans = (ans + dp[i][j]) % Mod
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		self.mod = 1000000000.0 + 7
		self.cache = {}
		self.knight_steps = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		count = 0
		for i in range(10):
			count += self.recursive_calc(i, n - 1)
			count = count % self.mod
		return int(count % self.mod)

	def recursive_calc(self, current_number, steps):
		if steps == 0:
			return 1
		if (current_number, steps) in self.cache:
			return self.cache[current_number, steps]
		total = 0
		for i in self.knight_steps[current_number]:
			total += self.recursive_calc(i, steps - 1)
			total = total % self.mod
		self.cache[current_number, steps] = total
		return self.cache[current_number, steps]


class Solution:

	def knightDialer(self, n: int) -> int:
		self.ans = dict()
		self.ans[0] = 10
		board = [[1] * 3 for _ in range(4)]
		board[3][0] = board[3][2] = 0
		pre_dict = {(i, j): self.prevMove(i, j) for i in range(4) for j in range(3)}
		for n in range(1, n):
			new_board = copy.deepcopy(board)
			for i in range(4):
				for j in range(3):
					cur_move = 0
					for (x, y) in pre_dict[i, j]:
						cur_move = (cur_move + board[x][y]) % (10 ** 9 + 7)
					new_board[i][j] = cur_move
			board = new_board
		return sum([board[i][j] for i in range(4) for j in range(3)]) % (10 ** 9 + 7)

	def prevMove(self, i, j):
		if (i, j) == (3, 0) or (i, j) == (3, 2):
			return []
		directions = [(-2, 1), (-1, 2), (1, 2), (2, 1), (2, -1), (1, -2), (-1, -2), (-2, -1)]
		res = []
		for d in directions:
			(x, y) = (i + d[0], j + d[1])
			if 0 <= x < 4 and 0 <= y < 3 and ((x, y) != (3, 0)) and ((x, y) != (3, 2)):
				res.append((x, y))
		return res


from functools import lru_cache

class Solution:

	def knightDialer(self, N: int) -> int:

		@lru_cache(None)
		def _jump(row, col, remaining):
			if remaining == 1:
				return 1
			total = 0
			for (dr, dc) in ((2, 1), (2, -1), (-2, 1), (-2, -1), (1, 2), (1, -2), (-1, 2), (-1, -2)):
				if 0 <= row + dr < m and 0 <= col + dc < n and pad[row + dr][col + dc]:
					total += _jump(row + dr, col + dc, remaining - 1)
			return total % MAX
		MAX = 10 ** 9 + 7
		pad = [[1, 1, 1], [1, 1, 1], [1, 1, 1], [0, 1, 0]]
		(m, n) = (len(pad), len(pad[0]))
		total = 0
		for i in range(m):
			for j in range(n):
				if pad[i][j]:
					total += _jump(i, j, N)
		return total % MAX


class Solution:

	def knightDialer(self, N: int) -> int:
		total = 0
		places = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		if N == 1:
			return 10
		dp = [1] * 10
		for i in range(2, N + 1):
			tmp_dp = [0] * 10
			for i in range(0, 10):
				if i != 5:
					neighbors = places.get(i)
					curr = 0
					for n in neighbors:
						curr += dp[n]
					tmp_dp[i] = curr
			dp = copy.deepcopy(tmp_dp)
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def __init__(self):
		self.memory = {}

	def knightDialer(self, n: int) -> int:
		steps = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 9, 3], 5: [], 6: [7, 1, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		def kDialer(i, n, steps, c):
			if n == 1:
				return 1
			if n == 0:
				return 0
			if (i, n) in self.memory:
				return self.memory[i, n]
			self.memory[i, n] = 0
			for j in steps[i]:
				self.memory[i, n] += kDialer(j, n - 1, steps, c) % c
			self.memory[i, n] = self.memory[i, n] % c
			return self.memory[i, n]
		combinations = 0
		for i in range(0, 10):
			combinations += kDialer(i, n, steps, 10 ** 9 + 7) % (10 ** 9 + 7)
		return combinations % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = {(0, 0): 1, (0, 1): 1, (0, 2): 1, (1, 0): 1, (1, 1): 1, (1, 2): 1, (2, 0): 1, (2, 1): 1, (2, 2): 1, (3, 1): 1}
		for x in range(1, n):
			temp = {}
			for r in range(4):
				for c in range(3):
					if r == 3 and c == 0 or (r == 3 and c == 2):
						continue
					sm = 0
					for i in (1, -1):
						for j in (2, -2):
							sm = sm + dp.get((r + i, c + j), 0) + dp.get((r + j, c + i), 0)
					temp[r, c] = sm
			dp = temp
		return sum(dp.values()) % (10 ** 9 + 7)


from functools import reduce

def make_grid():
	g = [[1] * 3 for _ in range(4)]
	g[3][0] = None
	g[3][2] = None
	return g
MOVES = [(2, 1), (2, -1), (1, 2), (1, -2), (-1, 2), (-1, -2), (-2, 1), (-2, -1)]

def jump(grid):
	new_grid = make_grid()
	for i in range(4):
		for j in range(3):
			if grid[i][j] is not None:
				c = 0
				for (di, dj) in MOVES:
					ni = i + di
					nj = j + dj
					if 0 <= ni < 4 and 0 <= nj < 3 and (grid[ni][nj] is not None):
						c += grid[ni][nj]
				new_grid[i][j] = c
	return new_grid

class Solution:

	def knightDialer(self, n: int) -> int:
		grid = make_grid()
		m = 10 ** 9 + 7
		c = 0
		for _ in range(n - 1):
			grid = jump(grid)
			c += 10
		print(grid)
		return sum([sum([c for c in row if c]) for row in grid]) % m


class Solution:

	def knightDialer(self, n: int) -> int:
		limit = 10 ** 9 + 7
		direction = [(1, 2), (-1, 2), (1, -2), (-1, -2), (2, -1), (2, 1), (-2, 1), (-2, -1)]
		dp = [[1 for i in range(3)] for j in range(4)]
		(dp[3][0], dp[3][2]) = (0, 0)
		for i in range(n - 1):
			temp = [[0 for i in range(3)] for j in range(4)]
			for i in range(4):
				for j in range(3):
					if i == 3 and j != 1:
						continue
					for (di, dj) in direction:
						(new_i, new_j) = (di + i, dj + j)
						if 0 <= new_i < 4 and 0 <= new_j < 3:
							temp[i][j] = (temp[i][j] + dp[new_i][new_j]) % limit
			dp = temp[:]
		res = 0
		for i in range(4):
			for j in range(3):
				res += dp[i][j]
		return res % limit


class Solution:
	dic = {}
	dic[1] = [6, 8]
	dic[2] = [7, 9]
	dic[3] = [4, 8]
	dic[4] = [0, 3, 9]
	dic[5] = []
	dic[6] = [0, 1, 7]
	dic[7] = [2, 6]
	dic[8] = [1, 3]
	dic[9] = [2, 4]
	dic[0] = [4, 6]

	def knightDialer(self, n: int) -> int:
		mem = defaultdict(int)
		for j in range(10):
			mem[1, j] = 1
		for i in range(1, n):
			for j in range(10):
				for num in self.dic[j]:
					mem[i + 1, num] += mem[i, j]
					mem[i + 1, num] = mem[i + 1, num] % (10 ** 9 + 7)
		res = 0
		for i in range(10):
			res += mem[n, i]
			res = res % (10 ** 9 + 7)
		return res


class Solution:

	def knightDialer(self, N: int) -> int:
		MOD = 10 ** 9 + 7
		dp = [[0] * 3 for _2 in range(4)]
		for i in range(4):
			for j in range(3):
				if (i, j) in [(3, 0), (3, 2)]:
					continue
				dp[i][j] = 1
		for k in range(1, N):
			new_dp = [[0] * 3 for _2 in range(4)]
			for i in range(3):
				for j in range(i, 3):
					a = [[i + 2, j + 1], [i + 2, j - 1], [i - 2, j + 1], [i - 2, j - 1], [i + 1, j + 2], [i - 1, j + 2], [i + 1, j - 2], [i - 1, j - 2]]
					for p in a:
						if not 0 <= p[0] < 4 or not 0 <= p[1] < 3:
							continue
						new_dp[i][j] += dp[p[0]][p[1]] % MOD
			new_dp[1][0] = new_dp[1][2]
			new_dp[2][0] = new_dp[2][2]
			new_dp[2][1] = new_dp[0][1]
			i = 3
			j = 1
			new_dp[3][1] = (dp[1][2] + dp[1][0]) % MOD
			dp = new_dp
		s = 0
		for i in dp:
			for j in i:
				s += j % MOD
		return s % MOD


class Solution:

	def __init__(self):
		self.moves = [[4, 6], [8, 6], [7, 9], [4, 8], [9, 3, 0], [], [7, 1, 0], [6, 2], [1, 3], [2, 4]]
		self.memoized_results = {}

	def knightDialer(self, n: int) -> int:
		total_moves = 0
		for number in range(10):
			moves = self.knightDialerOnOneDigit(number, n - 1)
			total_moves += moves
		return total_moves % (pow(10, 9) + 7)

	def knightDialerOnOneDigit(self, current_number, remaining_moves):
		if remaining_moves == 0:
			return 1
		moves = 0
		for number in self.moves[current_number]:
			if (number, remaining_moves - 1) in list(self.memoized_results.keys()):
				new_moves = self.memoized_results[number, remaining_moves - 1]
			else:
				new_moves = self.knightDialerOnOneDigit(number, remaining_moves - 1)
				self.memoized_results[number, remaining_moves - 1] = new_moves
			moves += new_moves
		return moves


MOD = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:

		@lru_cache(None)
		def dfs(i, j, k):
			if k == n - 1:
				return 1
			res = 0
			for (di, dj) in [(-2, -1), (-2, 1), (2, -1), (2, 1), (-1, -2), (-1, 2), (1, -2), (1, 2)]:
				(ni, nj) = (i + di, j + dj)
				if not (0 <= ni < 4 and 0 <= nj < 3):
					continue
				if (ni, nj) in [(3, 0), (3, 2)]:
					continue
				res += dfs(ni, nj, k + 1)
				res %= MOD
			return res
		ans = 0
		for (i, j) in product(range(4), range(3)):
			if (i, j) in [(3, 0), (3, 2)]:
				continue
			ans += dfs(i, j, 0)
		return ans % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		M = 4
		N = 3
		KMOD = 10 ** 9 + 7
		dp = [[1 for _ in range(N)] for _ in range(M)]
		dp[3][0] = dp[3][2] = 0
		directions = [(1, 2), (-1, -2), (1, -2), (-1, 2), (2, 1), (-2, -1), (2, -1), (-2, 1)]
		for _ in range(1, n):
			cur = [[0 for _ in range(N)] for _ in range(M)]
			for i in range(M):
				for j in range(N):
					if i == 3 and (j == 0 or j == 2):
						continue
					for d in directions:
						x = i + d[0]
						y = j + d[1]
						if 0 <= x < M and 0 <= y < N:
							cur[i][j] += dp[x][y]
			dp = cur
		result = 0
		for i in range(M):
			for j in range(N):
				if i == 3 and (j == 0 or j == 2):
					continue
				result += dp[i][j]
		return result % KMOD


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 0:
			return 0
		dialer = [[1, 1, 1] for _ in range(4)]
		directions = [[-1, 2], [-2, 1], [-2, -1], [-1, -2], [1, -2], [2, -1], [2, 1], [1, 2]]
		forbidden = set()
		forbidden.add((3, 0))
		forbidden.add((3, 2))
		for _ in range(1, N):
			tmp = [[0, 0, 0] for _ in range(4)]
			for i in range(4):
				for j in range(3):
					if (i, j) not in forbidden:
						for direction in directions:
							(new_i, new_j) = (i + direction[0], j + direction[1])
							if 0 <= new_i < 4 and 0 <= new_j < 3:
								tmp[new_i][new_j] += dialer[i][j]
			dialer = tmp
		return (sum(sum(dialer, [])) - dialer[3][0] - dialer[3][2]) % (10 ** 9 + 7)


class Solution(object):

	def knightDialer(self, N):
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		MOD = 10 ** 9 + 7
		table = [1] * 10
		for _ in range(N - 1):
			temp = [0] * 10
			for (node, count) in enumerate(table):
				for nei in moves[node]:
					temp[nei] += count
					temp[nei] % MOD
			table = temp
		return sum(table) % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [(-2, 1), (-1, 2), (1, 2), (2, 1), (2, -1), (1, -2), (-1, -2), (-2, -1)]
		previous = {(r, c): 1 for (r, c) in ((0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 1))}
		current = {(r, c): 0 for (r, c) in previous}
		for i in range(n - 1):
			for ((r, c), v) in previous.items():
				for (dr, dc) in moves:
					if (r + dr, c + dc) in current:
						current[r + dr, c + dc] += v
						current[r + dr, c + dc] %= 1000000007
			previous = current
			current = {(r, c): 0 for (r, c) in previous}
		return sum(previous.values()) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		keyboard = [[0] * 3 for _ in range(4)]
		k = 1
		for i in range(3):
			for j in range(3):
				keyboard[i][j] = k
				k += 1
		keyboard[-1][0] = -1
		keyboard[-1][-1] = -1
		mod = 10 ** 9 + 7
		count = [[1] * 3 for _ in range(4)]
		count[-1][0] = 0
		count[-1][-1] = 0
		moves = [(2, 1), (2, -1), (-2, 1), (-2, -1), (1, 2), (-1, 2), (1, -2), (-1, -2)]
		for k in range(n - 1):
			tmp_count = [[0] * 3 for _ in range(4)]
			for i in range(4):
				for j in range(3):
					if keyboard[i][j] < 0:
						continue
					for mv in moves:
						x = i + mv[0]
						y = j + mv[1]
						if 0 <= x < 4 and 0 <= y < 3 and (keyboard[x][y] >= 0):
							tmp_count[x][y] = (tmp_count[x][y] + count[i][j]) % mod
			count = tmp_count
		num_count = 0
		for r in count:
			num_count = (num_count + sum(r)) % mod
		return num_count


class Solution:
	mod = 10 ** 9 + 7
	phone = [[1, 1, 1], [1, 1, 1], [1, 1, 1], [0, 1, 0]]
	moves = ((2, 1), (1, 2), (2, -1), (1, -2), (-2, 1), (-1, 2), (-2, -1), (-1, -2))

	def knightDialer(self, n: int) -> int:

		@lru_cache(None)
		def helper(row, col, left):
			if left <= 0:
				return 1
			ans = 0
			for (r, c) in Solution.moves:
				if 0 <= row + r <= 3 and 0 <= col + c <= 2 and (Solution.phone[row + r][col + c] == 1):
					ans += helper(row + r, col + c, left - 1)
			return ans
		ans = 0
		for row in range(4):
			for col in range(3):
				if Solution.phone[row][col] == 1:
					ans += helper(row, col, n - 1)
		return ans % Solution.mod


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		(f1, f2, f3, f4, f6, f7, f8, f9, f0) = ([1] * n, [1] * n, [1] * n, [1] * n, [1] * n, [1] * n, [1] * n, [1] * n, [1] * n)
		for j in range(1, n):
			f0[j] = (f4[j - 1] + f6[j - 1]) % (1000000000.0 + 7)
			f1[j] = (f6[j - 1] + f8[j - 1]) % (1000000000.0 + 7)
			f2[j] = (f7[j - 1] + f9[j - 1]) % (1000000000.0 + 7)
			f3[j] = (f4[j - 1] + f8[j - 1]) % (1000000000.0 + 7)
			f4[j] = (f3[j - 1] + f9[j - 1] + f0[j - 1]) % (1000000000.0 + 7)
			f6[j] = (f1[j - 1] + f7[j - 1] + f0[j - 1]) % (1000000000.0 + 7)
			f7[j] = (f6[j - 1] + f2[j - 1]) % (1000000000.0 + 7)
			f8[j] = (f1[j - 1] + f3[j - 1]) % (1000000000.0 + 7)
			f9[j] = (f2[j - 1] + f4[j - 1]) % (1000000000.0 + 7)
		res = f0[n - 1] + f1[n - 1] + f2[n - 1] + f3[n - 1] + f7[n - 1] + f8[n - 1] + f9[n - 1] + f4[n - 1] + f6[n - 1]
		return int(res % (1000000000.0 + 7))


class Solution:

	def knightDialer(self, n: int) -> int:
		N = n
		transition = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		self.count = 0
		self.mem = {}

		def dfs(cur, steps):
			if steps == 2:
				return len(transition[cur])
			else:
				tmp = 0
				if (cur, steps) in self.mem:
					return self.mem[cur, steps]
				for neigh in transition[cur]:
					tmp += dfs(neigh, steps - 1)
				self.mem[cur, steps] = tmp
				return self.mem[cur, steps]
		if N == 1:
			return 10
		for i in range(10):
			self.count += dfs(i, N)
		return self.count % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:

		def dp(cur: int, k: int, cache: dict) -> int:
			state = tuple([cur, k])
			if state in cache:
				return cache[state]
			if k == 0:
				return 1
			dic = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [0, 1, 7], [2, 6], [1, 3], [2, 4]]
			res = 0
			for nc in dic[cur]:
				res += dp(nc, k - 1, cache)
			cache[state] = res
			return cache[state]
		result = 0
		cache = {}
		mod = 10 ** 9 + 7
		for i in range(10):
			result += dp(i, n - 1, cache)
			result = result % mod
		return result % mod


class Solution:

	def knightDialer(self, n: int) -> int:
		memo = {}
		return sum((self.hopper(i, n - 1, memo) for i in range(10))) % (10 ** 9 + 7)

	def hopper(self, cur_ind, hops_left, memo):
		if hops_left == 0:
			return 1
		if (cur_ind, hops_left) in memo:
			return memo[cur_ind, hops_left]
		counts = 0
		for nbr in self.nbrs(cur_ind):
			res = self.hopper(nbr, hops_left - 1, memo)
			counts += res
			memo[nbr, hops_left - 1] = res
		return counts

	def nbrs(self, ind):
		nbrs = {0: [4, 6], 1: [6, 8], 2: [9, 7], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [4, 2]}
		return nbrs[ind]


from functools import reduce

class Solution:
	validMoves = {0: {4, 6}, 1: {6, 8}, 2: {7, 9}, 3: {4, 8}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

	def knightDialer(self, n: int) -> int:
		cache = {}

		def reducer(acc: int, x: int) -> int:
			return (acc + x) % 1000000007

		def helper(remainingMoves: int, location: int) -> int:
			depth = n - remainingMoves
			insert = '\\t' * depth
			if remainingMoves == 0:
				return 1
			elif (remainingMoves, location) in cache:
				answer = cache[remainingMoves, location]
				return answer
			else:
				nextMoves = self.validMoves[location]
				answers = [helper(remainingMoves - 1, newLocation) for newLocation in nextMoves]
				reduced = reduce(reducer, answers, 0)
				cache[remainingMoves, location] = reduced
				return reduced
		answers = [helper(n - 1, x) for x in range(0, 10)]
		reduced = reduce(reducer, answers, 0)
		return reduced


class Solution:

	def knightDialer(self, n: int) -> int:
		grid = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [-1, 0, -1]]
		(R, C) = (len(grid), len(grid[0]))
		dp = [[1] * C for _ in range(R)]
		invalid = set([(3, 0), (3, 2)])
		for (r, c) in invalid:
			dp[r][c] = 0
		dirs = [(2, 1), (-2, 1), (2, -1), (-2, -1), (1, 2), (-1, 2), (1, -2), (-1, -2)]
		for _ in range(n - 1):
			dp2 = [[0] * C for _ in range(R)]
			for (r, row) in enumerate(dp):
				for (c, val) in enumerate(row):
					if (r, c) in invalid:
						continue
					for (dr, dc) in dirs:
						(nr, nc) = (r + dr, c + dc)
						if (nr, nc) in invalid:
							continue
						if 0 <= nr < R and 0 <= nc < C:
							dp2[nr][nc] += val
			dp = dp2
		return sum(map(sum, dp)) % (pow(10, 9) + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		(m, n) = (4, 3)
		dp = {}
		ans = 0
		for k in range(1, N + 1):
			count = 0
			for i in range(m):
				for j in range(n):
					if i == 3 and j in [0, 2]:
						continue
					temp = 0
					if 1 == k:
						temp += 1
					else:
						for (a, b) in [(2, 1), (2, -1), (-2, 1), (-2, -1), (1, 2), (1, -2), (-1, 2), (-1, -2)]:
							(r, c) = (i + a, j + b)
							if 0 <= r < m and 0 <= c < n and ((r, c) not in [(3, 0), (3, 2)]):
								temp += dp[r, c, k - 1]
					dp[i, j, k] = temp
					count += temp
			ans = count
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		if n == 1:
			return 10
		for i in range(n - 1):
			dpc = dp[:]
			dpc[0] = dp[4] + dp[6]
			dpc[1] = dp[6] + dp[8]
			dpc[2] = dp[7] + dp[9]
			dpc[3] = dp[4] + dp[8]
			dpc[4] = dp[9] + dp[3] + dp[0]
			dpc[5] = 0
			dpc[6] = dp[7] + dp[1] + dp[0]
			dpc[7] = dp[6] + dp[2]
			dpc[8] = dp[1] + dp[3]
			dpc[9] = dp[2] + dp[4]
			dp = dpc
		return sum(dp) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		dp = [[None] * 10 for _ in range(N + 1)]
		edges = [[1, 6], [1, 8], [2, 7], [2, 9], [3, 4], [3, 8], [4, 9], [4, 0], [6, 7], [6, 0]]
		graph = {}
		for (edge0, edge1) in edges:
			graph[edge0] = graph.get(edge0, []) + [edge1]
			graph[edge1] = graph.get(edge1, []) + [edge0]

		def count(n, x):
			if n == 0:
				return 1
			if dp[n][x] is not None:
				return dp[n][x]
			dp[n][x] = sum([count(n - 1, y) for y in graph.get(x, [])])
			return dp[n][x]
		return sum([count(N - 1, x) for x in range(10)]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		arr = [1] * 10
		mul = [[0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0]]
		for n in range(N - 1):
			newarr = [0] * 10
			for i in range(10):
				for j in range(10):
					newarr[i] += mul[i][j] * arr[j]
					newarr[i] %= 10 ** 9 + 7
			arr = newarr
		s = 0
		for x in arr:
			s = (s + x) % (10 ** 9 + 7)
		return s


class Solution:

	def knightDialer(self, N: int) -> int:
		d = {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2), (3, 1)}
		dirs = [(-2, -1), (-2, 1), (2, -1), (2, 1), (-1, 2), (1, 2), (-1, -2), (1, -2)]
		m = 10 ** 9 + 7
		dp = {}
		for x in d:
			dp[x] = [0] * (N + 1)
			dp[x][1] = 1
		for n in range(2, N + 1):
			for (r, c) in d:
				for z in dirs:
					(rz, cz) = (r + z[0], c + z[1])
					if (rz, cz) in d:
						dp[r, c][n] = (dp[r, c][n] + dp[rz, cz][n - 1]) % m
		return sum((x[N] for x in dp.values())) % m


class Solution:

	def knightDialer(self, n: int) -> int:

		@lru_cache(None)
		def dp(i, j, k):
			if k == 0:
				return 1
			result = 0
			for di in [-2, -1, 1, 2]:
				for dj in [3 - abs(di), abs(di) - 3]:
					(ii, jj) = (i + di, j + dj)
					if 0 <= ii < m and 0 <= jj < n and (not (ii == 3 and (jj == 0 or jj == 2))):
						result = (result + dp(ii, jj, k - 1)) % MOD
			return result
		MOD = 10 ** 9 + 7
		k = n
		(m, n) = (4, 3)
		result = 0
		for i in range(m):
			for j in range(n):
				if i == 3 and (j == 0 or j == 2):
					continue
				result = (result + dp(i, j, k - 1)) % MOD
		return result


class Solution:

	def knightDialer(self, left: int) -> int:
		moves = [(2, -1), (2, 1), (-2, 1), (-2, -1), (-1, 2), (-1, -2), (1, 2), (1, -2)]
		n = 4
		m = 3

		@lru_cache(None)
		def back(i, j, left):
			if left == 1:
				return 1
			ans = 0
			for (a, b) in moves:
				if 0 <= i + a < n and 0 <= j + b < m and ((i + a, j + b) != (3, 0)) and ((i + a, j + b) != (3, 2)):
					ans += back(i + a, j + b, left - 1)
			return ans
		main = 0
		for i in range(3):
			for j in range(3):
				main += back(i, j, left)
		main += back(3, 1, left)
		return main % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:

		def knightPos(i, j):
			lt = (i + 2, j - 1)
			lb = (i - 2, j - 1)
			rt = (i + 2, j + 1)
			rb = (i - 2, j + 1)
			tl = (i + 1, j - 2)
			tr = (i + 1, j + 2)
			bl = (i - 1, j - 2)
			br = (i - 1, j + 2)
			return (lt, lb, rt, rb, tl, tr, bl, br)
		dp = [[1] * 3 for _ in range(4)]
		dp[3][0] = dp[3][2] = 0
		mod = 10 ** 9 + 7
		for k in range(1, n):
			tmp = [[0] * 3 for _ in range(4)]
			for i in range(4):
				for j in range(3):
					if i == 3 and j == 0 or (i == 3 and j == 2):
						continue
					for (x, y) in knightPos(i, j):
						if 0 <= x <= 3 and 0 <= y <= 2:
							tmp[i][j] += dp[x][y]
			dp = tmp
		return sum([sum(i) for i in dp]) % mod


class Solution:

	@lru_cache(maxsize=None)
	def startFrom(self, i, l):
		if l <= 1:
			return 1 if l == 1 else 0
		else:
			return sum([self.startFrom(j, l - 1) for j in self.mapping[i]]) % (10 ** 9 + 7)

	def knightDialer(self, n: int) -> int:
		self.mapping = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		return sum([self.startFrom(i, n) for i in range(10)]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		ans = [1 for x in range(10)]
		mod = 1000000007
		for i in range(n - 1):
			(ans[0], ans[1], ans[2], ans[3], ans[4], ans[5], ans[6], ans[7], ans[8], ans[9]) = (ans[4] + ans[6], ans[8] + ans[6], ans[7] + ans[9], ans[8] + ans[4], ans[9] + ans[3] + ans[0], 0, ans[7] + ans[1] + ans[0], ans[6] + ans[2], ans[1] + ans[3], ans[4] + ans[2])
		return sum(ans) % mod


class Solution:
	from collections import defaultdict

	def knightDialer(self, N: int) -> int:
		pos_mapping = [[4, 6], [6, 8], [9, 7], [4, 8], [9, 3, 0], [], [7, 1, 0], [6, 2], [1, 3], [4, 2]]
		total_count = 0
		for i in range(10):
			prev_arr = [0] * 10
			prev_arr[i] = 1
			for ii in range(N - 1):
				new_arr = [0] * 10
				for (idx, count) in enumerate(prev_arr):
					if count == 0:
						continue
					for next_pos in pos_mapping[idx]:
						new_arr[next_pos] += count
				prev_arr = new_arr
			total_count += sum(prev_arr)
		MOD = 10 ** 9 + 7
		return total_count % MOD


class Solution:

	def knightDialer(self, N: int) -> int:
		dirs = [(2, 1), (1, 2), (2, -1), (1, -2), (-2, -1), (-1, -2), (-2, 1), (-1, 2)]
		dp = [[0 for j in range(N)] for i in range(10)]
		for num in range(10):
			dp[num][0] = 1
		for i in range(1, N):
			for num in range(10):
				if num == 0:
					pos = (1, 3)
				else:
					pos = ((num - 1) % 3, (num - 1) // 3)
				x = pos[0]
				y = pos[1]
				for d in dirs:
					new_x = x - d[0]
					new_y = y - d[1]
					if new_x < 0 or new_x > 2 or new_y < 0 or (new_y > 3):
						continue
					if new_x == 0 and new_y == 3 or (new_x == 2 and new_y == 3):
						continue
					new_num = 0 if new_x == 1 and new_y == 3 else new_y * 3 + new_x + 1
					dp[num][i] += dp[new_num][i - 1]
		res = 0
		for num in range(10):
			res += dp[num][N - 1]
		return res % (pow(10, 9) + 7)


class Solution:

	def helper(self, n, board, row, col, cache):
		if n == 0:
			return 1
		if (row, col, n) in cache:
			return cache[row, col, n]
		rows = len(board)
		cols = len(board[0])
		result = 0
		for (rMove, cMove) in [(-1, -2), (-2, -1), (2, 1), (1, 2), (-2, 1), (1, -2), (2, -1), (-1, 2)]:
			if 0 <= row + rMove < rows and 0 <= col + cMove < cols and (board[row + rMove][col + cMove] not in ['*', '#']):
				result += self.helper(n - 1, board, row + rMove, col + cMove, cache)
		cache[row, col, n] = result
		return result

	def knightDialer(self, n: int) -> int:
		board = [['1', '2', '3'], ['4', '5', '6'], ['7', '8', '9'], ['*', '0', '#']]
		totalResult = 0
		cache = {}
		rows = len(board)
		cols = len(board[0])
		for r in range(rows):
			for c in range(cols):
				if board[r][c] not in ['*', '#']:
					totalResult += self.helper(n - 1, board, r, c, cache)
		return totalResult % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		board = [[1, 2, 3], [4, 5, 6], [7, 8, 9], ['*', 0, '#']]
		dirc = [[-2, -1], [-2, 1], [-1, -2], [-1, 2], [1, -2], [1, 2], [2, -1], [2, 1]]
		mod = 10 ** 9 + 7
		mem = {}

		def dfs(i, j, k):
			if k == 1:
				return 1
			if (i, j, k) in mem:
				return mem[i, j, k]
			ans = 0
			for (x, y) in dirc:
				if -1 < i + x < 4 and -1 < j + y < 3 and (board[i + x][j + y] != '#') and (board[i + x][j + y] != '*'):
					ans += dfs(i + x, j + y, k - 1) % mod
			ans %= mod
			mem[i, j, k] = ans
			return ans
		res = 0
		for i in range(3):
			for j in range(3):
				res += dfs(i, j, n) % mod
		res = (res + dfs(3, 1, n)) % mod
		return res


class Solution:

	def knightDialer(self, N: int) -> int:
		cac = {}
		MOD = 10 ** 9 + 7
		pmvs = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [4, 2]]

		def d(k, i):
			try:
				return cac[k, i]
			except:
				pass
			if k == 0:
				return 1
			s = 0
			for j in pmvs[i]:
				s += d(k - 1, j) % MOD
			cac[k, i] = s % MOD
			return cac[k, i]
		ans = 0
		for i in range(10):
			ans += d(N - 1, i) % MOD
		return ans % MOD


class Solution:

	def __init__(self):
		self.helper = {(1, 2), (1, -2), (-1, 2), (-1, -2), (2, 1), (2, -1), (-2, 1), (-2, -1)}

	def dynamic(self, r, c, dp):
		curr = 0
		for s in self.helper:
			(x, y) = (r + s[0], c + s[1])
			if 0 <= x < 4 and 0 <= y < 3 and ((x, y) != (3, 0) or (x, y) != (3, 2)):
				curr += dp[x][y]
		return curr

	def knightDialer(self, n: int) -> int:
		dp = [[1] * 3 for _ in range(4)]
		dp[3][0] = dp[3][2] = 0
		for i in range(n - 1):
			dp2 = [[0] * 3 for _ in range(4)]
			for r in range(4):
				for c in range(3):
					if (r, c) == (3, 0) or (r, c) == (3, 2):
						continue
					dp2[r][c] = self.dynamic(r, c, dp)
			dp = dp2[:]
		return sum([dp[i][j] for i in range(4) for j in range(3)]) % (10 ** 9 + 7)


class Solution:
	adjacency = {0: {4, 6}, 1: {8, 6}, 2: {7, 9}, 3: {8, 4}, 4: {3, 9, 0}, 5: {}, 6: {1, 7, 0}, 7: {2, 6}, 8: {1, 3}, 9: {2, 4}}

	def matrixExponentiation(self, a: List[List[int]], k: int) -> List[List[int]]:
		if k == 0:
			return [[1 if r == c else 0 for c in range(len(a[0]))] for r in range(len(a))]
		result = self.matrixExponentiation(a, k // 2)
		result = self.matrixMultiplication(result, result)
		if k % 2 == 1:
			result = self.matrixMultiplication(a, result)
		return result

	def matrixMultiplication(self, a: List[List[int]], b: List[List[int]]) -> List[List[int]]:
		(m, n, p) = (len(a), len(a[0]), len(b[0]))
		assert len(a[0]) == len(b)
		matrix = [[0] * p for _ in range(m)]
		for r in range(m):
			for c in range(p):
				for i in range(n):
					matrix[r][c] += a[r][i] * b[i][c]
		return matrix

	def knightDialer(self, n: int):
		matrix = [[1 if r in Solution.adjacency[c] else 0 for c in range(10)] for r in range(10)]
		matrix = self.matrixExponentiation(matrix, n - 1)
		count = [[1] for _ in range(10)]
		count = self.matrixMultiplication(matrix, count)
		return sum((sum(r) for r in count)) % (10 ** 9 + 7)

	def knightDialerDP(self, n: int):
		count = [1 for _ in range(10)]
		for _ in range(n - 1):
			count = [sum((count[next_digit] for next_digit in Solution.adjacency[digit])) for digit in range(10)]
		return sum(count) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		nos = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [None, 0, None]]
		if N == 0:
			return 0
		memo = {}

		def calculate(currentIndex, remainingSteps):
			if remainingSteps == 0:
				return 1
			if (currentIndex, remainingSteps) in memo:
				return memo[currentIndex, remainingSteps]
			(i, j) = currentIndex
			possibleMoves = []
			if i + 2 < 4 and j - 1 >= 0 and (nos[i + 2][j - 1] is not None):
				possibleMoves.append((i + 2, j - 1))
			if i + 2 < 4 and j + 1 < 3 and (nos[i + 2][j + 1] is not None):
				possibleMoves.append((i + 2, j + 1))
			if i - 1 >= 0 and j + 2 < 3 and (nos[i - 1][j + 2] is not None):
				possibleMoves.append((i - 1, j + 2))
			if i + 1 < 4 and j + 2 < 3 and (nos[i + 1][j + 2] is not None):
				possibleMoves.append((i + 1, j + 2))
			if i - 2 >= 0 and j + 1 < 3 and (nos[i - 2][j + 1] is not None):
				possibleMoves.append((i - 2, j + 1))
			if i - 2 >= 0 and j - 1 >= 0 and (nos[i - 2][j - 1] is not None):
				possibleMoves.append((i - 2, j - 1))
			if i - 1 >= 0 and j - 2 >= 0 and (nos[i - 1][j - 2] is not None):
				possibleMoves.append((i - 1, j - 2))
			if i + 1 < 4 and j - 2 >= 0 and (nos[i + 1][j - 2] is not None):
				possibleMoves.append((i + 1, j - 2))
			if remainingSteps == 1:
				memo[currentIndex, remainingSteps] = len(possibleMoves)
				return len(possibleMoves)
			totalNos = 0
			for nextInd in possibleMoves:
				if (nextInd, remainingSteps - 1) in memo:
					totalNos += memo[nextInd, remainingSteps - 1]
				else:
					totalNos += calculate(nextInd, remainingSteps - 1)
			memo[currentIndex, remainingSteps] = totalNos
			return memo[currentIndex, remainingSteps]
		total = 0
		for i in range(0, 4):
			for j in range(0, 3):
				if nos[i][j] is not None:
					total += calculate((i, j), N - 1)
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		P = 10 ** 9 + 7

		def wrap(x):
			return x - P if x >= P else x
		s = 0
		for k in range(10):
			d = [0] * 10
			d2 = [0] * 10
			d[k] = 1
			for i in range(n - 1):
				d2[0] = wrap(d[4] + d[6])
				d2[1] = wrap(d[6] + d[8])
				d2[2] = wrap(d[7] + d[9])
				d2[3] = wrap(d[4] + d[8])
				d2[4] = wrap(d[3] + d[9] + d[0])
				d2[5] = 0
				d2[6] = wrap(d[1] + d[7] + d[0])
				d2[7] = wrap(d[2] + d[6])
				d2[8] = wrap(d[1] + d[3])
				d2[9] = wrap(d[2] + d[4])
				(d, d2) = (d2, d)
			s += sum(d)
		return s % (10 ** 9 + 7)


class Solution:
	DIAL = [[1, 2, 3], [4, 5, 6], [7, 8, 9], ['*', 0, '#']]

	def knightDialer(self, n: int) -> int:
		directions = [(1, -2), (2, -1), (2, 1), (1, 2), (-1, 2), (-2, 1), (-2, -1), (-1, -2)]
		count = 0
		m = len(self.DIAL)
		nn = len(self.DIAL[0])
		cache = {}

		def jump(i, j, path_length):
			if path_length == n:
				return 1
			else:
				total = 0
				if (i, j, path_length) in cache:
					return cache[i, j, path_length]
				for (inc_r, inc_c) in directions:
					r = i + inc_r
					c = j + inc_c
					if 0 <= r < m and 0 <= c < nn and isinstance(self.DIAL[r][c], int):
						total += jump(r, c, path_length + 1)
				cache[i, j, path_length] = total
				return total
		res = 0
		for i in range(m):
			for j in range(nn):
				if isinstance(self.DIAL[i][j], int):
					res += jump(i, j, 1)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		modulo = 10 ** 9 + 7
		self.count = 0
		self.cache = {}
		for digit in range(0, 10):
			self.count += self.getWays(digit, n - 1)
		return self.count % modulo

	def getWays(self, digit, n):
		if n == 0:
			return 1
		if (digit, n) in self.cache:
			return self.cache[digit, n]
		temp = 0
		for neighbor in self.neighbors(digit):
			temp += self.getWays(neighbor, n - 1)
		self.cache[digit, n] = temp
		return self.cache[digit, n]

	def neighbors(self, digit):
		neighbors = {0: (4, 6), 1: (6, 8), 2: (7, 9), 3: (4, 8), 4: (0, 3, 9), 5: (), 6: (0, 1, 7), 7: (2, 6), 8: (1, 3), 9: (2, 4)}
		return neighbors[digit]


import math

class Solution:

	def knightDialer(self, N: int) -> int:
		dp = [[[0 for _ in range(3)] for _ in range(4)] for _ in range(N)]
		direction = [(1, 2), (1, -2), (-1, 2), (-1, -2), (2, 1), (2, -1), (-2, 1), (-2, -1)]
		for k in range(N):
			for i in range(4):
				for j in range(3):
					if k == 0:
						if i == 3 and j == 0 or (i == 3 and j == 2):
							dp[0][i][j] = None
						else:
							dp[0][i][j] = 1
					else:
						if dp[k - 1][i][j] == None:
							dp[k][i][j] = None
							continue
						if i == 1 and j == 1:
							dp[k][i][j] = 0
							continue
						for d in direction:
							fromi = i + d[0]
							fromj = j + d[1]
							if 0 <= fromi <= 3 and 0 <= fromj <= 2 and (dp[k - 1][fromi][fromj] != None):
								dp[k][i][j] += dp[k - 1][fromi][fromj]
		res = 0
		for i in range(4):
			for j in range(3):
				if dp[-1][i][j] == None:
					continue
				res += dp[-1][i][j]
		t = pow(10, 9) + 7
		return res % t


class Solution:

	def __init__(self):
		self.memo = {}

	def getOrCreate(self, i, n):
		if (i, n) not in self.memo:
			self.memo[i, n] = self.__knightDialerDP(i, n)
		return self.memo[i, n]

	def __knightDialerDP(self, i, n):
		if n == 0:
			return 0
		if n == 1:
			return 1
		if i == 0:
			return self.getOrCreate(4, n - 1) + self.getOrCreate(6, n - 1)
		elif i == 1:
			return self.getOrCreate(6, n - 1) + self.getOrCreate(8, n - 1)
		elif i == 2:
			return self.getOrCreate(7, n - 1) + self.getOrCreate(9, n - 1)
		elif i == 3:
			return self.getOrCreate(4, n - 1) + self.getOrCreate(8, n - 1)
		elif i == 4:
			return self.getOrCreate(0, n - 1) + self.getOrCreate(3, n - 1) + self.getOrCreate(9, n - 1)
		elif i == 6:
			return self.getOrCreate(0, n - 1) + self.getOrCreate(1, n - 1) + self.getOrCreate(7, n - 1)
		elif i == 7:
			return self.getOrCreate(2, n - 1) + self.getOrCreate(6, n - 1)
		elif i == 8:
			return self.getOrCreate(1, n - 1) + self.getOrCreate(3, n - 1)
		elif i == 9:
			return self.getOrCreate(2, n - 1) + self.getOrCreate(4, n - 1)
		else:
			return 0

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		for k in range(n):
			total_count = 0
			for i in range(10):
				total_count += self.__knightDialerDP(i, k + 1)
		return total_count % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		mod = 10 ** 9 + 7
		for i in range(1, n):
			dp_old = dp.copy()
			dp[0] = dp_old[4] + dp_old[6]
			dp[1] = dp_old[6] + dp_old[8]
			dp[2] = dp_old[7] + dp_old[9]
			dp[3] = dp_old[4] + dp_old[8]
			dp[4] = dp_old[3] + dp_old[9] + dp_old[0]
			dp[5] = 0
			dp[6] = dp_old[1] + dp_old[7] + dp_old[0]
			dp[7] = dp_old[2] + dp_old[6]
			dp[8] = dp_old[1] + dp_old[3]
			dp[9] = dp_old[2] + dp_old[4]
		return sum(dp) % mod


class Solution:

	def helper(self, cache, position, num_hops):
		neighbors = [[4, 6], [6, 8], [7, 9], [4, 8], [3, 9, 0], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		if (position, num_hops) in cache:
			return cache[position, num_hops]
		if num_hops == 0:
			return 1
		else:
			num_sequences = 0
			for neighbor in neighbors[position]:
				num_sequences += self.helper(cache, neighbor, num_hops - 1)
			cache[position, num_hops] = num_sequences
		return num_sequences

	def knightDialer(self, n: int) -> int:
		cache = {}
		res = 0
		for start in range(10):
			res += self.helper(cache, start, n - 1)
		return res % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		movesMap = dict()
		MOD = 10 ** 9 + 7
		movesMap[0] = [4, 6]
		movesMap[1] = [6, 8]
		movesMap[2] = [7, 9]
		movesMap[3] = [4, 8]
		movesMap[4] = [0, 3, 9]
		movesMap[5] = []
		movesMap[6] = [0, 1, 7]
		movesMap[7] = [2, 6]
		movesMap[8] = [1, 3]
		movesMap[9] = [2, 4]
		totalCount = 0
		for i in range(10):
			curPos = [0] * 10
			curPos[i] = 1
			for count in range(n - 1):
				nextPos = [0] * 10
				for curIndex in range(10):
					if curPos[curIndex] > 0:
						for nextIndex in movesMap[curIndex]:
							nextPos[nextIndex] += curPos[curIndex]
							nextPos[nextIndex] = nextPos[nextIndex] % MOD
				curPos = nextPos
			for finIndex in range(10):
				totalCount += curPos[finIndex]
				totalCount = totalCount % MOD
		return totalCount


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		pad = [['1', '2', '3'], ['4', '5', '6'], ['7', '8', '9'], ['*', '0', '#']]
		dirs = [[-1, -2], [-2, -1], [1, -2], [2, -1], [-1, 2], [-2, 1], [1, 2], [2, 1]]
		memo = dict()
		for i in range(10):
			memo[str(i)] = [0 for j in range(n + 1)]
			memo[str(i)][1] = 1
		for j in range(2, n + 1):
			for r in range(4):
				for c in range(3):
					number = pad[r][c]
					if number == '*' or number == '#':
						continue
					memo[number][j] = 0
					for dir0 in dirs:
						x = r + dir0[0]
						y = c + dir0[1]
						if x < 0 or x >= 4 or y < 0 or (y >= 3) or (pad[x][y] == '*') or (pad[x][y] == '#'):
							continue
						parent = pad[x][y]
						memo[number][j] += memo[parent][j - 1]
		res = 0
		for i in range(10):
			number = str(i)
			res += memo[number][n]
		return res % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		moves = [(x, y) for x in range(-2, 3, 2) for y in range(-2, 3, 2) if abs(x) != abs(y)]
		MOD = 10 ** 9 + 7
		res = 0
		mappings = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}

		@lru_cache
		def dfs(num_jumps, cell):
			if num_jumps == 1:
				return 1
			cur = 0
			for i in mappings[cell]:
				cur += dfs(num_jumps - 1, i)
			return cur
		for i in range(0, 10):
			res += dfs(n, i)
		return res % MOD


class Solution:

	def knightDialer(self, n: int) -> int:
		dialer_map = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}
		total = 0
		for i in range(10):
			if i == 5 and n == 1:
				total += 1
				continue
			level = {i: 1}
			curr = 1
			while curr < n:
				next_level = defaultdict(lambda : 0)
				for l in list(level.keys()):
					for d in dialer_map[l]:
						next_level[d] += level[l]
				level = next_level
				curr += 1
			count = sum(level.values())
			total += count
			total = total % (10 ** 9 + 7)
		return total


class Solution:

	def knightDialer(self, n: int) -> int:
		mod = 10 ** 9 + 7
		dp = [1] * 10
		for _ in range(2, n + 1):
			dpc = dp.copy()
			dp[0] = dpc[4] + dpc[6]
			dp[1] = dpc[6] + dpc[8]
			dp[2] = dpc[7] + dpc[9]
			dp[3] = dpc[4] + dpc[8]
			dp[4] = dpc[3] + dpc[9] + dpc[0]
			dp[5] = 0
			dp[6] = dpc[1] + dpc[7] + dpc[0]
			dp[7] = dpc[2] + dpc[6]
			dp[8] = dpc[1] + dpc[3]
			dp[9] = dpc[4] + dpc[2]
		res = sum(dp) % mod
		return res


class Solution:

	def knightDialer(self, n: int) -> int:
		valid_positions = {(0, 0): 1, (1, 0): 2, (2, 0): 3, (0, 1): 4, (1, 1): 5, (2, 1): 6, (0, 2): 7, (1, 2): 8, (2, 2): 9, (1, 3): 0}
		mod_val = 10 ** 9 + 7
		cache = {}

		def find_numbers(start, length):
			if start not in valid_positions:
				return 0
			(x, y) = start
			if (x, y, length) in cache:
				return cache[x, y, length]
			if length == n:
				return 1
			(x, y) = start
			nums_found = sum([find_numbers((x + 1, y - 2), length + 1), find_numbers((x + 2, y - 1), length + 1), find_numbers((x - 1, y - 2), length + 1), find_numbers((x - 2, y - 1), length + 1), find_numbers((x - 2, y + 1), length + 1), find_numbers((x - 1, y + 2), length + 1), find_numbers((x + 2, y + 1), length + 1), find_numbers((x + 1, y + 2), length + 1)]) % mod_val
			cache[x, y, length] = nums_found
			return nums_found
		numbers_found = 0
		for position in valid_positions:
			numbers_found += find_numbers(position, 1)
			numbers_found %= mod_val
		return numbers_found


class Solution:

	def knightDialer(self, n: int) -> int:
		self.mod = 10 ** 9 + 7
		total_path = 0
		self.d = {}
		for i in range(0, 4):
			for j in range(0, 3):
				total_path = (total_path + self.dfs(i, j, n)) % self.mod
		return total_path

	def dfs(self, i, j, n):
		if i < 0 or j < 0 or j >= 3 or (i >= 4) or (i == 3 and j != 1):
			return 0
		if (i, j, n) in self.d:
			return self.d[i, j, n]
		if n == 1:
			return 1
		total = self.dfs(i - 1, j + 2, n - 1) % self.mod + self.dfs(i - 1, j - 2, n - 1) % self.mod + self.dfs(i + 1, j - 2, n - 1) % self.mod + self.dfs(i + 1, j + 2, n - 1) % self.mod + self.dfs(i + 2, j + 1, n - 1) % self.mod + self.dfs(i + 2, j - 1, n - 1) % self.mod + self.dfs(i - 2, j + 1, n - 1) % self.mod + self.dfs(i - 2, j - 1, n - 1) % self.mod
		self.d[i, j, n] = total
		return total


class Solution:

	def knightDialer(self, N: int) -> int:
		memo = {}
		maxi = 10 ** 9 + 7

		def paths(i, j, n):
			if i > 3 or j > 2 or i < 0 or (j < 0) or (i == 3 and j != 1):
				return 0
			if n == 1:
				return 1
			if (i, j, n) in memo:
				return memo[i, j, n]
			result = paths(i - 1, j - 2, n - 1) % maxi + paths(i - 2, j - 1, n - 1) % maxi + paths(i - 2, j + 1, n - 1) % maxi + paths(i - 1, j + 2, n - 1) % maxi + paths(i + 1, j + 2, n - 1) % maxi + paths(i + 2, j + 1, n - 1) % maxi + paths(i + 2, j - 1, n - 1) % maxi + paths(i + 1, j - 2, n - 1) % maxi
			memo[i, j, n] = result
			return result
		totalPaths = 0
		for i in range(4):
			for j in range(3):
				totalPaths = (totalPaths + paths(i, j, N)) % maxi
		return totalPaths


class Solution:

	def knightDialer(self, N: int) -> int:
		total = 0
		places = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 6: [1, 7, 0], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		if N == 1:
			return 10
		dp = [1] * 10
		for i in range(2, N + 1):
			tmp = copy.deepcopy(dp)
			for i in range(0, 10):
				if i != 5:
					vals = places.get(i)
					new_tot = 0
					for v in vals:
						new_tot += dp[v]
					tmp[i] = new_tot
			dp = copy.deepcopy(tmp)
		ans = 0
		for d in dp:
			ans += d
		return (ans - 1) % (10 ** 9 + 7)


class Solution:

	def nextPositions(self, n):
		(x, y) = self.x_y_map[n]
		arr = [(x - 2, y + 1), (x - 1, y + 2), (x + 1, y + 2), (x + 2, y + 1), (x + 2, y - 1), (x + 1, y - 2), (x - 1, y - 2), (x - 2, y - 1)]
		return [self.reverse_map[v] for v in arr if v in self.reverse_map]

	def build_x_y_map(self):
		(r, c) = (0, 0)
		ht = {}
		for i in range(1, 10):
			ht[i] = (r, c)
			c += 1
			if c == 3:
				r += 1
				c = 0
		ht[0] = (3, 1)
		return ht

	def knightDialer(self, n: int) -> int:
		self.x_y_map = self.build_x_y_map()
		self.reverse_map = {v: k for (k, v) in list(self.x_y_map.items())}

		def count_moves(curr_cell, hops, memo):
			if hops == 0:
				return 1
			key = (curr_cell, hops)
			if key not in memo:
				ways = 0
				for pos in self.nextPositions(curr_cell):
					ways += count_moves(pos, hops - 1, memo)
				memo[key] = ways
			return memo[key]
		total = 0
		memo = {}
		for i in range(0, 10):
			total += count_moves(i, n - 1, memo)
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		keyboard = [[1, 2, 3], [4, 5, 6], [7, 8, 9], [-1, 0, -1]]
		dp = [[[1, 1, 1], [1, 1, 1], [1, 1, 1], [0, 1, 0]]]
		modulo = 10 ** 9 + 7
		for k in range(1, n):
			dp.append([[0 for _ in range(3)] for _ in range(4)])
			for i in range(4):
				for j in range(3):
					for (x, y) in [(i + 2, j + 1), (i + 2, j - 1), (i - 2, j + 1), (i - 2, j - 1), (i + 1, j + 2), (i + 1, j - 2), (i - 1, j + 2), (i - 1, j - 2)]:
						if 0 <= x < 4 and 0 <= y < 3 and (keyboard[x][y] != -1):
							dp[k][x][y] = (dp[k][x][y] + dp[k - 1][i][j]) % modulo
		return sum((sum(row) for row in dp[n - 1])) % modulo


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return 0
		if n == 1:
			return 10
		total = 9
		digit = {}
		for j in range(0, 10):
			if j == 5:
				continue
			digit[j] = 1
		const = 10 ** 9 + 7
		for i in range(1, n):
			num_1 = (digit[6] + digit[8]) % const
			num_2 = (digit[7] + digit[9]) % const
			num_3 = (digit[4] + digit[8]) % const
			num_4 = (digit[3] + digit[9] + digit[0]) % const
			num_6 = (digit[1] + digit[7] + digit[0]) % const
			num_7 = (digit[2] + digit[6]) % const
			num_8 = (digit[1] + digit[3]) % const
			num_9 = (digit[2] + digit[4]) % const
			num_0 = (digit[4] + digit[6]) % const
			digit[0] = num_0
			digit[1] = num_1
			digit[2] = num_2
			digit[3] = num_3
			digit[4] = num_4
			digit[6] = num_6
			digit[7] = num_7
			digit[8] = num_8
			digit[9] = num_9
			total = (num_0 + num_1 + num_2 + num_3 + num_4 + num_6 + num_7 + num_8 + num_9) % const
		return total


class Solution:

	def knightDialer(self, n: int) -> int:
		path = {0: [4, 6], 1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4]}

		@lru_cache
		def paths(i, n):
			if n == 1:
				return len(path[i])
			if n == 0:
				return 1
			s = 0
			for v in path[i]:
				s += paths(v, n - 1)
			return s
		ans = 0
		for k in path:
			ans += paths(k, n - 1)
		return ans % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		D = [[0] * 10 for _ in range(2)]
		D[0] = [1] * 10
		for i in range(1, N):
			idx = i % 2
			P = D[(i - 1) % 2]
			D[idx][1] = P[8] + P[6]
			D[idx][2] = P[7] + P[9]
			D[idx][3] = P[4] + P[8]
			D[idx][4] = P[3] + P[9] + P[0]
			D[idx][5] = 0
			D[idx][6] = P[1] + P[7] + P[0]
			D[idx][7] = P[2] + P[6]
			D[idx][8] = P[1] + P[3]
			D[idx][9] = P[2] + P[4]
			D[idx][0] = P[4] + P[6]
		return sum(D[(N + 1) % 2]) % (10 ** 9 + 7)


mexp = 10 ** 9 + 7

class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1 for x in range(10)]
		for _ in range(n - 1):
			ndp = [0 for x in range(10)]
			ndp[0] = (dp[4] + dp[6]) % mexp
			ndp[1] = (dp[6] + dp[8]) % mexp
			ndp[2] = (dp[7] + dp[9]) % mexp
			ndp[3] = (dp[4] + dp[8]) % mexp
			ndp[4] = (dp[3] + dp[9] + dp[0]) % mexp
			ndp[5] = 0
			ndp[6] = (dp[1] + dp[7] + dp[0]) % mexp
			ndp[7] = (dp[2] + dp[6]) % mexp
			ndp[8] = (dp[1] + dp[3]) % mexp
			ndp[9] = (dp[2] + dp[4]) % mexp
			dp = ndp
		return sum(dp) % mexp


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		a_0 = 1
		a_1 = 1
		a_2 = 1
		a_3 = 1
		a_4 = 1
		a_5 = 0
		a_6 = 1
		a_7 = 1
		a_8 = 1
		a_9 = 1
		A = [a_0, a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9]

		def count_next_moves(A):
			result = []
			result.append(A[6] + A[4])
			result.append(A[6] + A[8])
			result.append(A[7] + A[9])
			result.append(A[4] + A[8])
			result.append(A[3] + A[9] + A[0])
			result.append(0)
			result.append(A[1] + A[7] + A[0])
			result.append(A[6] + A[2])
			result.append(A[1] + A[3])
			result.append(A[2] + A[4])
			return result
		for i in range(n - 1):
			A = count_next_moves(A)
		result = sum(A) % (10 ** 9 + 7)
		return result


class Solution:

	def knightDialer(self, N: int) -> int:
		if N == 1:
			return 10
		ends_in = [0 if i == 5 else 1 for i in range(10)]
		mod = 1000000000.0 + 7
		for i in range(N - 1):
			next_ends_in = [0 for _ in range(10)]
			next_ends_in[0] = (ends_in[4] + ends_in[6]) % mod
			next_ends_in[1] = (ends_in[6] + ends_in[8]) % mod
			next_ends_in[2] = (ends_in[7] + ends_in[9]) % mod
			next_ends_in[3] = (ends_in[4] + ends_in[8]) % mod
			next_ends_in[4] = (ends_in[3] + ends_in[9] + ends_in[0]) % mod
			next_ends_in[6] = (ends_in[1] + ends_in[7] + ends_in[0]) % mod
			next_ends_in[7] = (ends_in[2] + ends_in[6]) % mod
			next_ends_in[8] = (ends_in[1] + ends_in[3]) % mod
			next_ends_in[9] = (ends_in[2] + ends_in[4]) % mod
			ends_in = next_ends_in
		return int(sum(ends_in) % mod)


class Solution:

	def knightDialer(self, n: int) -> int:
		dp = [1] * 10
		MOD = 10 ** 9 + 7
		for i in range(2, n + 1):
			old_dp = dp.copy()
			dp[0] = old_dp[4] + old_dp[6]
			dp[1] = old_dp[6] + old_dp[8]
			dp[2] = old_dp[7] + old_dp[9]
			dp[3] = old_dp[4] + old_dp[8]
			dp[4] = old_dp[3] + old_dp[9] + old_dp[0]
			dp[5] = 0
			dp[6] = old_dp[1] + old_dp[7] + old_dp[0]
			dp[7] = old_dp[2] + old_dp[6]
			dp[8] = old_dp[1] + old_dp[3]
			dp[9] = old_dp[2] + old_dp[4]
		ans = sum(dp) % MOD
		return ans


class Solution:

	def knightDialer(self, n: int) -> int:
		dialer = {}
		for i in range(10):
			dialer[i] = 1
		for j in range(n):
			store = [dialer[k] for k in dialer]
			dialer[0] = store[4] + store[6]
			dialer[1] = store[8] + store[6]
			dialer[2] = store[9] + store[7]
			dialer[3] = store[8] + store[4]
			dialer[4] = store[0] + store[9] + store[3]
			dialer[5] = 0
			dialer[6] = store[0] + store[7] + store[1]
			dialer[7] = store[2] + store[6]
			dialer[8] = store[1] + store[3]
			dialer[9] = store[2] + store[4]
		return sum(store) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		len_start_number = {}
		mod_num = 1000000007
		len_start_number = {(1, i): 1 for i in range(0, 10)}
		for i in range(2, n + 1):
			len_start_number[i, 1] = (len_start_number[i - 1, 4] + len_start_number[i - 1, 8]) % mod_num
			len_start_number[i, 2] = len_start_number[i - 1, 7] * 2 % mod_num
			len_start_number[i, 4] = (len_start_number[i - 1, 1] + len_start_number[i - 1, 7] + len_start_number[i - 1, 0]) % mod_num
			len_start_number[i, 5] = 0
			len_start_number[i, 7] = (len_start_number[i - 1, 2] + len_start_number[i - 1, 4]) % mod_num
			len_start_number[i, 8] = len_start_number[i - 1, 1] * 2 % mod_num
			len_start_number[i, 0] = len_start_number[i - 1, 4] * 2 % mod_num
		count = 0
		for k in [0, 1, 2, 4, 5, 7, 8]:
			if k in [1, 4, 7]:
				count += 2 * len_start_number[n, k] % mod_num
			else:
				count += len_start_number[n, k] % mod_num
		return count % mod_num


import numpy as np

class Solution:

	def knightDialer(self, n: int) -> int:
		M = np.matrix([[0, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0, 0, 0, 0, 0]])
		dp = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
		f = M
		n = n - 1
		while n > 0:
			if n % 2:
				dp = dp * M % 1000000007
			n = n // 2
			M = M * M % 1000000007
		return np.sum(dp) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 1:
			return 10
		chessmap = {1: [4, 2], 2: [1, 3], 3: [4, 2], 4: [3, 1, 0], 0: [4, 4]}
		table = [1] * 5
		for i in range(2, n + 1):
			tmp = [0] * 5
			for j in range(5):
				for k in chessmap[j]:
					tmp[j] += table[k]
			table = tmp
		return (sum(table) * 2 - table[0]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, l: int) -> int:
		dpTable = [1] * 10
		for _ in range(l - 1):
			newTable = [0] * 10
			for i in [0, 1, 2, 3, 4, 6, 7, 8, 9]:
				if i == 0:
					ret = dpTable[4] + dpTable[6]
				elif i == 1:
					ret = dpTable[6] + dpTable[8]
				elif i == 2:
					ret = dpTable[7] + dpTable[9]
				elif i == 3:
					ret = dpTable[4] + dpTable[8]
				elif i == 4:
					ret = dpTable[3] + dpTable[9] + dpTable[0]
				elif i == 6:
					ret = dpTable[1] + dpTable[7] + dpTable[0]
				elif i == 7:
					ret = dpTable[2] + dpTable[6]
				elif i == 8:
					ret = dpTable[1] + dpTable[3]
				elif i == 9:
					ret = dpTable[2] + dpTable[4]
				newTable[i] = ret % 1000000007
			dpTable = newTable
		return sum(dpTable) % 1000000007


class Solution:

	def knightDialer(self, N: int) -> int:
		D = 10 ** 9 + 7
		l = [1 for _ in range(10)]
		for _ in range(N - 1):
			l = self.transform_list(l)
			l = [x % D for x in l]
		return sum(l) % D

	def transform_list(self, l: List[int]) -> List[int]:
		nl = [0 for _ in range(10)]
		nl[0] = l[4] + l[6]
		nl[1] = l[6] + l[8]
		nl[2] = l[7] + l[9]
		nl[3] = l[4] + l[8]
		nl[4] = l[3] + l[9] + l[0]
		nl[6] = l[1] + l[7] + l[0]
		nl[7] = l[2] + l[6]
		nl[8] = l[1] + l[3]
		nl[9] = l[2] + l[4]
		return nl


class Solution:

	def knightDialer(self, n: int) -> int:
		if n == 0:
			return n
		pad = []
		for i in range(4):
			pad.append([1] * 3)
		pad[3][0] = 0
		pad[3][2] = 0
		for k in range(n - 1):
			newPad = []
			for i in range(4):
				newPad.append([1] * 3)
			newPad[0][0] = (pad[1][2] + pad[2][1]) % (10 ** 9 + 7)
			newPad[0][1] = (pad[2][0] + pad[2][2]) % (10 ** 9 + 7)
			newPad[0][2] = (pad[1][0] + pad[2][1]) % (10 ** 9 + 7)
			newPad[1][0] = (pad[0][2] + pad[2][2] + pad[3][1]) % (10 ** 9 + 7)
			newPad[1][1] = 0
			newPad[1][2] = (pad[0][0] + pad[2][0] + pad[3][1]) % (10 ** 9 + 7)
			newPad[2][0] = (pad[1][2] + pad[0][1]) % (10 ** 9 + 7)
			newPad[2][1] = (pad[0][0] + pad[0][2]) % (10 ** 9 + 7)
			newPad[2][2] = (pad[0][1] + pad[1][0]) % (10 ** 9 + 7)
			newPad[3][0] = 0
			newPad[3][1] = (pad[1][0] + pad[1][2]) % (10 ** 9 + 7)
			newPad[3][2] = 0
			pad = newPad
		total = 0
		for i in range(len(pad)):
			total += sum(pad[i])
		return total % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		dp = [[0] * 10 for _ in range(N)]
		for i in range(N):
			if i == 0:
				dp[i] = [1] * 10
				continue
			dp[i][0] = dp[i - 1][4] + dp[i - 1][6]
			dp[i][1] = dp[i - 1][8] + dp[i - 1][6]
			dp[i][2] = dp[i - 1][7] + dp[i - 1][9]
			dp[i][3] = dp[i - 1][4] + dp[i - 1][8]
			dp[i][4] = dp[i - 1][0] + dp[i - 1][3] + dp[i - 1][9]
			dp[i][5] = 0
			dp[i][6] = dp[i - 1][0] + dp[i - 1][1] + dp[i - 1][7]
			dp[i][7] = dp[i - 1][2] + dp[i - 1][6]
			dp[i][8] = dp[i - 1][1] + dp[i - 1][3]
			dp[i][9] = dp[i - 1][2] + dp[i - 1][4]
		return sum(dp[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, N: int) -> int:
		dp = [0] * 10
		for j in range(10):
			dp[j] = 1
		for i in range(1, N):
			tmp0 = (dp[4] + dp[6]) % (math.pow(10, 9) + 7)
			tmp1 = (dp[6] + dp[8]) % (math.pow(10, 9) + 7)
			tmp2 = (dp[7] + dp[9]) % (math.pow(10, 9) + 7)
			tmp3 = (dp[4] + dp[8]) % (math.pow(10, 9) + 7)
			tmp4 = (dp[0] + dp[3] + dp[9]) % (math.pow(10, 9) + 7)
			tmp5 = 0
			tmp6 = (dp[0] + dp[1] + dp[7]) % (math.pow(10, 9) + 7)
			tmp7 = (dp[2] + dp[6]) % (math.pow(10, 9) + 7)
			tmp8 = (dp[1] + dp[3]) % (math.pow(10, 9) + 7)
			tmp9 = (dp[2] + dp[4]) % (math.pow(10, 9) + 7)
			dp[0] = tmp0
			dp[1] = tmp1
			dp[2] = tmp2
			dp[3] = tmp3
			dp[4] = tmp4
			dp[5] = tmp5
			dp[6] = tmp6
			dp[7] = tmp7
			dp[8] = tmp8
			dp[9] = tmp9
		total = 0
		for j in range(10):
			if N > 1 and j == 5:
				continue
			total += dp[j]
		total = int(total % (math.pow(10, 9) + 7))
		return total


class Solution:

	def knightDialer(self, N: int) -> int:
		T = [[0] * (N + 1) for i in range(10)]
		for i in range(10):
			T[i][1] = 1
		for step in range(2, N + 1):
			T[0][step] = T[4][step - 1] + T[6][step - 1]
			T[1][step] = T[8][step - 1] + T[6][step - 1]
			T[2][step] = T[7][step - 1] + T[9][step - 1]
			T[3][step] = T[4][step - 1] + T[8][step - 1]
			T[4][step] = T[3][step - 1] + T[9][step - 1] + T[0][step - 1]
			T[5][step] = 0
			T[6][step] = T[1][step - 1] + T[7][step - 1] + T[0][step - 1]
			T[7][step] = T[6][step - 1] + T[2][step - 1]
			T[8][step] = T[1][step - 1] + T[3][step - 1]
			T[9][step] = T[2][step - 1] + T[4][step - 1]
		return sum([T[i][N] for i in range(10)]) % (pow(10, 9) + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		num = 0
		stack = [(1, i, i) for i in range(10)]
		pos = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		memo = [[1] * 10 for _ in range(n)]
		for i in range(1, n):
			memo[i][0] = memo[i - 1][4] + memo[i - 1][6]
			memo[i][1] = memo[i - 1][6] + memo[i - 1][8]
			memo[i][2] = memo[i - 1][7] + memo[i - 1][9]
			memo[i][3] = memo[i - 1][4] + memo[i - 1][8]
			memo[i][4] = memo[i - 1][0] + memo[i - 1][3] + memo[i - 1][9]
			memo[i][5] = 0
			memo[i][6] = memo[i - 1][1] + memo[i - 1][7] + memo[i - 1][0]
			memo[i][7] = memo[i - 1][2] + memo[i - 1][6]
			memo[i][8] = memo[i - 1][1] + memo[i - 1][3]
			memo[i][9] = memo[i - 1][2] + memo[i - 1][4]
		return sum(memo[-1]) % (10 ** 9 + 7)


class Solution:

	def knightDialer(self, n: int) -> int:
		moveable = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [0, 3, 9], 5: [], 6: [0, 1, 7], 7: [2, 6], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		MOD = 7 + 1000000000.0
		dp = [1] * 10
		for step in range(n - 1):
			newDP = [0] * 10
			for key in range(10):
				for move in moveable[key]:
					newDP[move] = (newDP[move] + dp[key]) % MOD
			dp = newDP
		return int(sum(dp) % MOD)


class Solution:

	def knightDialer(self, n: int) -> int:
		jump = {1: [6, 8], 2: [7, 9], 3: [4, 8], 4: [3, 9, 0], 5: [], 6: [1, 7, 0], 7: [6, 2], 8: [1, 3], 9: [2, 4], 0: [4, 6]}
		dp = [1] * 10
		for _ in range(n - 1):
			newDp = [1] * 10
			for i in range(10):
				res = 0
				for item in jump[i]:
					res += dp[item]
				res %= 1000000007
				newDp[i] = res
			dp = newDp
		return sum(dp) % 1000000007


class Solution:

	def knightDialer(self, n: int) -> int:
		(a, M) = ([1] * 10, 10 ** 9 + 7)
		moves = [(4, 6), (6, 8), (7, 9), (4, 8), (0, 3, 9), (), (0, 1, 7), (2, 6), (1, 3), (2, 4)]
		for _ in range(1, n):
			b = [0] * 10
			for i in range(10):
				for j in moves[i]:
					b[i] = (b[i] + a[j]) % M
			a = b
		return sum(a) % M


class Solution:

	def knightDialer(self, N: int) -> int:
		dp = [1] * 10
		MOD = 10 ** 9 + 7
		moves = [[4, 6], [6, 8], [7, 9], [4, 8], [0, 3, 9], [], [1, 7, 0], [2, 6], [1, 3], [2, 4]]
		for hop in range(N - 1):
			new_dp = [0] * 10
			for (num, count) in enumerate(dp):
				for neigh in moves[num]:
					new_dp[neigh] = (new_dp[neigh] + count) % MOD
			dp = new_dp
		return sum(dp) % MOD