Alice is a beginner composer and now she is ready to create another masterpiece. And not even the single one but two at the same time! 

Alice has a sheet with n notes written on it. She wants to take two such non-empty non-intersecting subsequences that both of them form a melody and sum of their lengths is maximal.

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

Subsequence forms a melody when each two adjacent notes either differs by 1 or are congruent modulo 7.

You should write a program which will calculate maximum sum of lengths of such two non-empty non-intersecting subsequences that both of them form a melody.


-----Input-----

The first line contains one integer number n (2 ≤ n ≤ 5000).

The second line contains n integer numbers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^5) — notes written on a sheet.


-----Output-----

Print maximum sum of lengths of such two non-empty non-intersecting subsequences that both of them form a melody.


-----Examples-----
Input
4
1 2 4 5

Output
4

Input
6
62 22 60 61 48 49

Output
5



-----Note-----

In the first example subsequences [1, 2] and [4, 5] give length 4 in total.

In the second example subsequences [62, 48, 49] and [60, 61] give length 5 in total. If you choose subsequence [62, 61] in the first place then the second melody will have maximum length 2, that gives the result of 4, which is not maximal.

Source: codeforces | Difficulty: VERY_HARD
Tags: Dynamic programming

Flows and cuts


Solutions:
import sys
n = int(input()) + 1
a = [0] + list(map(int, input().split()))
mod7 = [x % 7 for x in a]
dp = [[0] * n for _ in range(n)]
maxnum = [0] * (10 ** 5 + 10)
ans = 0
for i in range(n):
	maxmod = [0] * 7
	for j in range(n):
		maxnum[a[j]] = 0
	for j in range(i):
		maxnum[a[j]] = max(maxnum[a[j]], dp[j][i])
		maxmod[mod7[j]] = max(maxmod[mod7[j]], dp[j][i])
	for j in range(i + 1, n):
		dp[i][j] = max(maxnum[a[j] - 1], maxnum[a[j] + 1], maxmod[mod7[j]], dp[0][i]) + 1
		maxnum[a[j]] = max(maxnum[a[j]], dp[i][j])
		maxmod[mod7[j]] = max(maxmod[mod7[j]], dp[i][j])
		ans = max(ans, dp[i][j])
print(ans)


import sys

def solve():
	n = int(sys.stdin.readline())
	a = [0] + [int(i) for i in sys.stdin.readline().split()]
	dp = [[0] * (n + 1) for i in range(n + 1)]
	ans = 0
	maxnum = [0] * (10 ** 5 + 2)
	maxmod = [0] * 7
	for y in range(n + 1):
		maxmod = [0] * 7
		for ai in a:
			maxnum[ai] = 0
		for i in range(y):
			maxmod[a[i] % 7] = max(maxmod[a[i] % 7], dp[i][y])
			maxnum[a[i]] = max(maxnum[a[i]], dp[i][y])
		for x in range(y + 1, n + 1):
			dp[x][y] = max(maxmod[a[x] % 7], maxnum[a[x] + 1], maxnum[a[x] - 1], dp[0][y]) + 1
			dp[y][x] = dp[x][y]
			maxmod[a[x] % 7] = max(maxmod[a[x] % 7], dp[x][y])
			maxnum[a[x]] = max(maxnum[a[x]], dp[x][y])
			ans = max(ans, dp[x][y])
	print(ans)
solve()