Problem1896--Vladik and cards

1896: Vladik and cards

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 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.

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