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Codeforces Round 384 (Div. 2) |
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Finished |

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binary search

bitmasks

brute force

dp

*2200

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E. Vladik and cards

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVladik 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
*c*_{k}cards with number*k*on them in the subsequence, than for all pairs of integers the condition |*c*_{i}-*c*_{j}| ≤ 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.

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