Problem: 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).

Solution (in PYTHON3):

Solution:
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)