CF743E.Vladik and cards

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 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.

弗拉迪克在回家的路上感到无聊，决定玩一个游戏。他取了 $n$ 张卡片，并将它们排成一列放在自己面前。每张卡片上都写有一个不超过 8 的正整数。他想找出满足以下两个条件的最长子序列：

• 子序列中数字 $1$ 到 $8$ 各自出现的次数之差至多为 $1$。形式化地说，若子序列中数字 $k$ 出现了 $c_k$ 次，则对任意一对整数 ，必须满足 $|c_i - c_j| \leq 1$。
• 若子序列中至少存在一张数字为 $x$ 的卡片，则子序列中所有数字为 $x$ 的卡片必须构成一个连续段（但该连续段在原序列中不一定是连续的）。例如，子序列 $[1,\,1,\,2,\,2]$ 满足该条件，而子序列 $[1,\,2,\,2,\,1]$ 不满足。注意：$[1,\,1,\,2,\,2]$ 并不满足第一个条件。

请帮助弗拉迪克找出满足上述两个条件的最长子序列的长度。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 1000$）—— 表示弗拉迪克序列中卡片的数量。

第二行包含 $n$ 个正整数（每个数均不超过 $8$）组成的序列—— 描述弗拉迪克的序列。

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

输出一个整数——即弗拉迪克序列中满足两个条件的最长子序列的长度。

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.

在第一个样例中，所有卡片上写的数字都相等，因此你最多只能取一张卡片，否则将违反第一个条件。