Two Rabbits，在一个长度是n的环形序列上，找一个不连续的回文序列的最大长度。详见具体内容

Two Rabbits

# 限制

Time Limit: 10000/5000 MS (Java/Others)
Memory Limit: 65535/65535 K (Java/Others)

# 描述

Long long ago, there lived two rabbits Tom and Jerry in the forest. On a sunny afternoon, they planned to play a game with some stones. There were $n$ stones on the ground and they were arranged as a clockwise ring. That is to say, the first stone was adjacent to the second stone and the n-th stone, and the second stone is adjacent to the first stone and the third stone, and so on. The weight of the i-th stone is ai.
The rabbits jumped from one stone to another. Tom always jumped clockwise, and Jerry always jumped anticlockwise.
At the beginning, the rabbits both choose a stone and stand on it. Then at each turn, Tom should choose a stone which have not been stepped by itself and then jumped to it, and Jerry should do the same thing as Tom, but the jumping direction is anti-clockwise.
For some unknown reason, at any time , the weight of the two stones on which the two rabbits stood should be equal. Besides, any rabbit couldn’t jump over a stone which have been stepped by itself. In other words, if the Tom had stood on the second stone, it cannot jump from the first stone to the third stone or from the n-the stone to the 4-th stone.
Please note that during the whole process, it was OK for the two rabbits to stand on a same stone at the same time.
Now they want to find out the maximum turns they can play if they follow the optimal strategy.

# 输入格式

The input contains at most $20$ test cases.
For each test cases, the first line contains a integer $n$ denoting the number of stones.
The next line contains $n$ integers separated by space, and the i-th integer $a_i$ denotes the weight of the i-th stone.$(1 \le n \le 1000, 1 \le a_i \le 1000)$
The input ends with $n = 0$.

# 输出格式

For each test case, print a integer denoting the maximum turns.

# 提示

For the second case, the path of the Tom is $1, 2, 3, 4$, and the path of Jerry is $1, 4, 3, 2$.
For the third case, the path of Tom is $1,2,3,4,5$ and the path of Jerry is $4,3,2,1,5$.

# 思路二

dp[a][b]是区间[a,b]内的最长回文子串的长度。注意状态转移。dp[a][b]的最长回文子串的长度是从dp[a+1][b],dp[a][b-1]中的最大值。如果num[a]和num[b]相等，那么前面得到的最大值还需要与dp[a+1][b-1]+2比较一下，dp[a][b]取最大值。