743_E. Vladik and cards_9146
Vladik was bored on his way home and decided to play the following game. He took n cards and put them in a row in front of himself. Every card has a positive integer number not exceeding 8 written on it. He decided to find the longest subsequence of cards which satisfies the following conditions:

  * the number of occurrences of each number from 1 to 8 in the subsequence doesn't differ by more then 1 from the number of occurrences of any other number. Formally, if there are ck cards with number k on them in the subsequence, than for all pairs of integers <image> the condition |ci - cj| ≤ 1 must hold. 
  * if there is at least one card with number x on it in the subsequence, then all cards with number x in this subsequence must form a continuous segment in it (but not necessarily a continuous segment in the original sequence). For example, the subsequence [1, 1, 2, 2] satisfies this condition while the subsequence [1, 2, 2, 1] doesn't. Note that [1, 1, 2, 2] doesn't satisfy the first condition. 



Please help Vladik to find the length of the longest subsequence that satisfies both conditions.

Input

The first line contains single integer n (1 ≤ n ≤ 1000) — the number of cards in Vladik's sequence.

The second line contains the sequence of n positive integers not exceeding 8 — the description of Vladik's sequence.

Output

Print single integer — the length of the longest subsequence of Vladik's sequence that satisfies both conditions.

Examples

Input

3
1 1 1


Output

1

Input

8
8 7 6 5 4 3 2 1


Output

8

Input

24
1 8 1 2 8 2 3 8 3 4 8 4 5 8 5 6 8 6 7 8 7 8 8 8


Output

17

Note

In the first sample all the numbers written on the cards are equal, so you can't take more than one card, otherwise you'll violate the first condition.
import copy

def solve():
    n = int(input())
    a = [int(c)-1 for c in input().split(' ')]

    nextcard = [[-1 for i in range(8)] for j in range(n)]
    for i in range(n-2, -1, -1):
        nextcard[i] = copy.copy(nextcard[i+1])
        nextcard[i][a[i+1]] = i+1

    jump = [[-1 for i in range(n+1)] for j in range(n)]
    for i in range(n):
        card = a[i]
        cpos = i
        j = 1
        
        while cpos != -1:
            jump[i][j] = cpos
            j+=1
            cpos = nextcard[cpos][card]

    #Find dp solution for range (val, val+1)
    def getLen(val):
        dp = [[-1 for i in range(1<<8)] for j in range(n+1)]
        dp[0][0] = 0

        for i in range(n):
            card = a[i]
            for comb in range(1<<8):
                if (comb & (1<<card)) == 0 and dp[i][comb] != -1:
                    ncomb = comb + (1<<card)
                    
                    if jump[i][val] != -1:
                        j = jump[i][val]+1
                        dp[j][ncomb] = max(dp[j][ncomb], dp[i][comb] + val)
                        
                    if jump[i][val+1] != -1:
                        j = jump[i][val+1]+1
                        dp[j][ncomb] = max(dp[j][ncomb], dp[i][comb] + val + 1)

                dp[i+1][comb] = max(dp[i+1][comb], dp[i][comb])

        return dp[n][(1<<8)-1]

    appear = [False for i in range(8)]
    for c in a:
        appear[c] = True

    result = 0
    for c in appear:
        result += int(c)

    #Finally binary search to find the result

    cur = 0
    for lev in range(9, -1, -1):
        tpow = (1<<lev)
        if cur + tpow < n:
            ret = getLen(cur + tpow)

            if(ret != -1):
                result = max(result, ret)
                cur += tpow

    return result

print(solve())





























Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.

### Description:
Vladik was bored on his way home and decided to play the following game. He took n cards and put them in a row in front of himself. Every card has a positive integer number not exceeding 8 written on it. He decided to find the longest subsequence of cards which satisfies the following conditions:

  * the number of occurrences of each number from 1 to 8 in the subsequence doesn't differ by more then 1 from the number of occurrences of any other number. Formally, if there are ck cards with number k on them in the subsequence, than for all pairs of integers <image> the condition |ci - cj| ≤ 1 must hold. 
  * if there is at least one card with number x on it in the subsequence, then all cards with number x in this subsequence must form a continuous segment in it (but not necessarily a continuous segment in the original sequence). For example, the subsequence [1, 1, 2, 2] satisfies this condition while the subsequence [1, 2, 2, 1] doesn't. Note that [1, 1, 2, 2] doesn't satisfy the first condition. 



Please help Vladik to find the length of the longest subsequence that satisfies both conditions.

Input

The first line contains single integer n (1 ≤ n ≤ 1000) — the number of cards in Vladik's sequence.

The second line contains the sequence of n positive integers not exceeding 8 — the description of Vladik's sequence.

Output

Print single integer — the length of the longest subsequence of Vladik's sequence that satisfies both conditions.

Examples

Input

3
1 1 1


Output

1

Input

8
8 7 6 5 4 3 2 1


Output

8

Input

24
1 8 1 2 8 2 3 8 3 4 8 4 5 8 5 6 8 6 7 8 7 8 8 8


Output

17

Note

In the first sample all the numbers written on the cards are equal, so you can't take more than one card, otherwise you'll violate the first condition.

### Input:
3
1 1 1

### Output:
1

### Input:
24
1 8 1 2 8 2 3 8 3 4 8 4 5 8 5 6 8 6 7 8 7 8 8 8

### Output:
17


### Code:
import copy

def solve():
    n = int(input())
    a = [int(c)-1 for c in input().split(' ')]

    nextcard = [[-1 for i in range(8)] for j in range(n)]
    for i in range(n-2, -1, -1):
        nextcard[i] = copy.copy(nextcard[i+1])
        nextcard[i][a[i+1]] = i+1

    jump = [[-1 for i in range(n+1)] for j in range(n)]
    for i in range(n):
        card = a[i]
        cpos = i
        j = 1
        
        while cpos != -1:
            jump[i][j] = cpos
            j+=1
            cpos = nextcard[cpos][card]

    #Find dp solution for range (val, val+1)
    def getLen(val):
        dp = [[-1 for i in range(1<<8)] for j in range(n+1)]
        dp[0][0] = 0

        for i in range(n):
            card = a[i]
            for comb in range(1<<8):
                if (comb & (1<<card)) == 0 and dp[i][comb] != -1:
                    ncomb = comb + (1<<card)
                    
                    if jump[i][val] != -1:
                        j = jump[i][val]+1
                        dp[j][ncomb] = max(dp[j][ncomb], dp[i][comb] + val)
                        
                    if jump[i][val+1] != -1:
                        j = jump[i][val+1]+1
                        dp[j][ncomb] = max(dp[j][ncomb], dp[i][comb] + val + 1)

                dp[i+1][comb] = max(dp[i+1][comb], dp[i][comb])

        return dp[n][(1<<8)-1]

    appear = [False for i in range(8)]
    for c in a:
        appear[c] = True

    result = 0
    for c in appear:
        result += int(c)

    #Finally binary search to find the result

    cur = 0
    for lev in range(9, -1, -1):
        tpow = (1<<lev)
        if cur + tpow < n:
            ret = getLen(cur + tpow)

            if(ret != -1):
                result = max(result, ret)
                cur += tpow

    return result

print(solve())




























