Zuma

$\texttt{Genos}$ 最近在他的手机上下载了祖玛游戏。在祖玛游戏里，存在 $n$ 个一行的宝石，第 $i$ 个宝石的颜色是 $C_i$。这个游戏的目标是尽快的消灭一行中所有的宝石。 在一秒钟，$\texttt{Genos}$ 能很快的挑选出这些有颜色的宝石中的一个回文的、连续的子串，并将这个子串移除。每当一个子串被删除后，剩余的宝石将连接在一起，形成一个新的行列。 你的任务是：求出把整个宝石串都移除的最短时间。 ### 输入格式 第一行包含一个整数 $n(1 \le n \le 500)$，表示宝石串的长度。第二行包含 $n$ 个被空格分开的整数，第 $i(1 \le i \le n)$ 个表示这行中第 $i$ 个珠子的颜色。 ### 输出格式 输出一个整数，把这行珠子移除的最短时间。 ### 样例说明 在第一个例子中，$\texttt{Genos}$ 可以在一秒钟就把这行珠子全部移走。在第二个例子中，$\texttt{Genos}$ 一次只能移走一个珠子，所以移走三个珠子花费他三秒。在第三个例子中，为了达到 $2$ 秒的最快时间，先移除回文串 $\texttt{4 4}$,再移除回文串 $\texttt{1 2 3 2 1}$。 感谢 @Administrator2004 提供的翻译

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 $ c_{i} $ . 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.

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 $ c_{i} $ ( $ 1<=c_{i}<=n $ ) — the color of the $ i $ -th gemstone in a line.

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

3
1 2 1

1

3
1 2 3

3

7
1 4 4 2 3 2 1

2

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.