Zuma

time limit per test 2 seconds memory limit per test 512 megabytes

链接：
vjudge：E-E
codeforces：cf-607-B-Zuma

区间DP

Description

Genos recently installed the game Zuma on his phone. In Zuma there exists a line of n gemstones, the i-th of which has color ci. The goal of the game is to destroy all the gemstones in the line as quickly as possible.

In one second, Genos is able to choose exactly one continuous substring of colored gemstones that is a palindrome and remove it from the line. After the substring is removed, the remaining gemstones shift to form a solid line again. What is the minimum number of seconds needed to destroy the entire line?

Let us remind, that the string (or substring) is called palindrome, if it reads same backwards or forward. In our case this means the color of the first gemstone is equal to the color of the last one, the color of the second gemstone is equal to the color of the next to last and so on.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 500) — the number of gemstones.

The second line contains n space-separated integers, the i-th of which is ci (1 ≤ ci ≤ n) — the color of the i-th gemstone in a line.

Output

Print a single integer — the minimum number of seconds needed to destroy the entire line.

input

3
1 2 1

output

1

input

3
1 2 3

output

3

input

7
1 4 4 2 3 2 1

output

2

Note

In the first sample, Genos can destroy the entire line in one second.

In the second sample, Genos can only destroy one gemstone at a time, so destroying three gemstones takes three seconds.

In the third sample, to achieve the optimal time of two seconds, destroy palindrome 4 4 first and then destroy palindrome 1 2 3 2 1.

题意：

第一行输入一个数 n
第二行输入n个数
删除一个回文串需要1s，将回文串全部删除最少需要多长时间，输出最短时间

解题思路：

一个区间更新的题，很常见了,但是写的时候就zz了

完整代码：

#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define inf 0x3ffffff
int dp[510][510];
int a[510];
int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        memset(dp,0,sizeof(dp));
        for(int i=0;i<n;i++)
            scanf("%d",&a[i]);
        for(int l=0;l<n;l++)
            for(int i=0;i<n-l;i++)
            {
                int j=i+l;
                dp[i][j]=inf;
                if(a[i]==a[j])
                {
                    if(i+1==j||i==j)
                        dp[i][j]=1;
                    else
                        dp[i][j]=dp[i+1][j-1];
                }
                for(int k=i;k<j;k++)
                    dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]);
            }
            printf("%d\n",dp[0][n-1]);
    }
    return 0;
}