CodeForces - 607B Zuma 区间dp

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.

Examples

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：题意：给你一个序列，每次可以消除一个回文序列，问你最少需要多少次操作可以删除这个序列

题解：算是模板题了

dp[l][r] = min(dp[l][r], dp[l][k] + dp[k + 1][r]);
 if(a[l] == a[k]) dp[l][r] = min(dp[l][r], dp[l + 1][k - 1] + dp[k + 1][r] + (l + 1 > k - 1));// 注意如果 l 到 k 之间还有就并上，如果l到k没有数了，就算一次

#include 
using namespace std;

const int N = 510;

int n, m;
int a[N], dp[N][N];

int main() {
	
	while(~scanf("%d", &n)) {
		memset(dp, 0, sizeof(dp));
		for(int i = 1; i <= n; i++) {
			scanf("%d", &a[i]);
			dp[i][i] = 1;
		}

		for(int len = 2; len <= n; len++) {
			for(int l = 1; l <= n - len + 1; l++) {
				int r = l + len - 1;
				dp[l][r]  = len;
				for(int k = l; k <= r; k++) {
					dp[l][r] = min(dp[l][r], dp[l][k] + dp[k + 1][r]);
					if(a[l] == a[k]) dp[l][r] = min(dp[l][r], dp[l + 1][k - 1] + dp[k + 1][r] + (l + 1 > k - 1));
 				}
			}
		}
		printf("%d\n", dp[1][n]);
	}
	return 0;
}