Omkar and Akmar are playing a game on a circular board with n (2 ≤ n ≤ 10^6) cells. The cells are numbered from 1 to n so that for each i (1 ≤ i ≤ n-1) cell i is adjacent to cell i+1 and cell 1 is adjacent to cell n. Initially, each cell is empty.

Omkar and Akmar take turns placing either an A or a B on the board, with Akmar going first. The letter must be placed on an empty cell. In addition, the letter cannot be placed adjacent to a cell containing the same letter. 

A player loses when it is their turn and there are no more valid moves.

Output the number of possible distinct games where both players play optimally modulo 10^9+7. Note that we only consider games where some player has lost and there are no more valid moves.

Two games are considered distinct if the number of turns is different or for some turn, the letter or cell number that the letter is placed on were different.

A move is considered optimal if the move maximizes the player's chance of winning, assuming the other player plays optimally as well. More formally, if the player who has to move has a winning strategy, they have to make a move after which they will still have a winning strategy. If they do not, they can make any move.

Input

The only line will contain an integer n (2 ≤ n ≤ 10^6) — the number of cells on the board.

Output

Output a single integer — the number of possible distinct games where both players play optimally modulo 10^9+7.

Examples

Input


2


Output


4


Input


69420


Output


629909355


Input


42069


Output


675837193

Note

For the first sample case, the first player has 4 possible moves. No matter what the first player plays, the second player only has 1 possible move, so there are 4 possible games.

Difficulty: VERY_HARD
Tags: Constructive algorithms

Geometry

String algorithms

Combinatorics

Complete search

Number theory

Game theory

Mathematics

Polynomials and generating functions
Skill types: Complete search

Starter code:

Solutions:
import sys
input = sys.stdin.readline
n = int(input())
mod = 10 ** 9 + 7
F = [0] * (n + 1)
F[0] = 1
for i in range(1, n + 1):
	F[i] = i * F[i - 1] % mod
iF = [0] * (n + 1)
iF[-1] = pow(F[-1], mod - 2, mod)
for i in range(n - 1, -1, -1):
	iF[i] = iF[i + 1] * (i + 1) % mod

def C(n, k):
	if k > n:
		return 0
	return F[n] * iF[n - k] * iF[k] % mod
ans = 0
for x in range((n + 1) // 2, n + 1):
	if x % 2:
		continue
	if x < n:
		cur = (C(x, n - x) + C(x - 1, n - x - 1)) % mod
	else:
		cur = 1
	cur = cur * 2 * F[x] % mod
	ans = (ans + cur) % mod
print(ans)


from sys import stdin, gettrace
if gettrace():

	def inputi():
		return input()
else:

	def input():
		return next(stdin)[:-1]

	def inputi():
		return stdin.buffer.readline()
MOD = 1000000007

def main():
	n = int(input())
	factorial = [1]
	for i in range(1, n + 1):
		factorial.append(factorial[-1] * i % MOD)
	res = 0
	for i in range((n + 1) // 2 + (n + 1) // 2 % 2, n + 1, 2):
		if i == n:
			res = (res + factorial[n]) % MOD
		else:
			num1 = factorial[i]
			denom1 = factorial[n - i] * factorial[2 * i - n] % MOD
			num2 = factorial[i - 1]
			denom2 = factorial[n - i - 1] * factorial[2 * i - n] % MOD
			res = (res + (pow(denom1, MOD - 2, MOD) * num1 + pow(denom2, MOD - 2, MOD) * num2) * factorial[i]) % MOD
	print(res * 2 % MOD)
main()


import sys
sys.stderr = sys.stdout
M = 10 ** 9 + 7

def modinv(a):
	r0 = a
	r1 = M
	s0 = 1
	s1 = 0
	t0 = 0
	t1 = 1
	while r1:
		q = r0 // r1
		(r0, r1) = (r1, r0 - q * r1)
		(s0, s1) = (s1, s0 - q * s1)
		(t0, t1) = (t1, t0 - q * t1)
	if s0 < M:
		s0 += M
	return s0

def choose(a, b, I):
	b = min(b, a - b)
	c = 1
	for i in range(b):
		c = c * (a - i) % M
		c = c * I[b - i] % M
	return c

def games(n):
	I = [None] * (n + 1)
	for i in range(1, n + 1):
		I[i] = modinv(i)
	s = 0
	k0 = (n + 3) // 4
	k1 = n // 2
	c = choose(2 * k0, n - 2 * k0, I)
	for i in range(2, 2 * k0):
		c = c * i % M
	s = c
	for k in range(k0, k1):
		k_2 = k * 2
		for i in (k_2 + 2, k_2 + 1, k_2 + 1, k_2, n - k_2, n - k_2 - 1):
			c = c * i % M
		k_4_n = k * 4 - n
		for j in (k_4_n + 1, k_4_n + 2, k_4_n + 3, k_4_n + 4):
			c = c * I[j] % M
		s = (s + c) % M
	return 2 * n * s % M

def main():
	n = readint()
	print(games(n))

def readint():
	return int(input())

def readinti():
	return map(int, input().split())

def readintt():
	return tuple(readinti())

def readintl():
	return list(readinti())

def readinttl(k):
	return [readintt() for _ in range(k)]

def readintll(k):
	return [readintl() for _ in range(k)]

def log(*args, **kwargs):
	print(*args, **kwargs, file=sys.__stderr__)
main()


from sys import stdin

def getInt():
	return int(stdin.readline().strip())

def bruteForce(n):
	x = [[i, j] for i in range(3) for j in range(3) if i != j]
	for k in range(2, n):
		x = [a + [i] for a in x for i in range(3) if i != a[-1] and (a[-1] != 0 or i != a[-2])]
	x = [z for z in x if z[0] != z[-1] and (z[0] != 0 or z[1] != z[-1]) and (z[-1] != 0 or z[0] != z[-2])]
	ans = 0
	for p in x:
		sc = len([z for z in p if z != 0])
		k = 1
		for i in range(1, sc + 1):
			k *= i
		ans += k
	return ans
P = 10 ** 9 + 7
fcache = [1]

def factorial(n):
	while len(fcache) <= n:
		fcache.append(fcache[-1] * len(fcache) % P)
	return fcache[n]

def binom(n, k):
	return factorial(n) * pow(factorial(k) * factorial(n - k), P - 2, P) % P

def simpler(n):
	ans = 0
	i = n % 2
	while i * 2 <= n:
		k = factorial(n - i)
		if i == 0:
			t = 1
		else:
			t = binom(n - i, i) + binom(n - 2 - (i - 1), i - 1)
		ans += 2 * k * t
		i += 2
	return ans % P
print(simpler(getInt()))