Author note: I think some of you might remember the problem "Two Melodies" from Eductational Codeforces Round 22. Now it's time to make it a bit more difficult!

Alice is a composer, and recently she had recorded two tracks that became very popular. Now she has got a lot of fans who are waiting for new tracks. 

This time Alice wants to form four melodies for her tracks.

Alice has a sheet with n notes written on it. She wants to take four such non-empty non-intersecting subsequences that all 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 differ by 1 or are congruent modulo 7.

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

Input

The first line contains one integer number n (4 ≤ n ≤ 3000).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105) — notes written on a sheet.

Output

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

Examples

Input

5
1 3 5 7 9


Output

4


Input

5
1 3 5 7 2


Output

5

Note

In the first example it is possible to compose 4 melodies by choosing any 4 notes (and each melody will consist of only one note).

In the second example it is possible to compose one melody with 2 notes — {1, 2}. Remaining notes are used in other three melodies (one note per each melody).

Source: codeforces | Difficulty: VERY_HARD
Tags: Graph algorithms

Flows and cuts


Solutions:
import sys
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)


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)