Description

A palindrome is a symmetrical string, that is, a string read identically from left to right as well as from right to left. You are to write a PRogram which, given a string, determines the minimal number of characters to be inserted into the string in order to obtain a palindrome.

As an example, by inserting 2 characters, the string “Ab3bd” can be transformed into a palindrome (“dAb3bAd” or “Adb3bdA”). However, inserting fewer than 2 characters does not produce a palindrome.

Input

Your program is to read from standard input. The first line contains one integer: the length of the input string N, 3 <= N <= 5000. The second line contains one string with length N. The string is formed from uppercase letters from ‘A’ to ‘Z’, lowercase letters from ‘a(chǎn)’ to ‘z’ and digits from ‘0’ to ‘9’. Uppercase and lowercase letters are to be considered distinct.

Output

Your program is to write to standard output. The first line contains one integer, which is the desired minimal number.

Sample Input

Sample Output

題意

給出一個(gè)字符串，問(wèn)最少添加幾個(gè)字符才能構(gòu)成一個(gè)回文串。

思路

對(duì)于這種類型的題目是有一個(gè)公式的啦！

添加的最少字符個(gè)數(shù) = 字符串長(zhǎng)度 - （字符串正序與逆序的最長(zhǎng)公共子序列長(zhǎng)度）

但是，對(duì)于這道題，僅僅知道這個(gè)公式可不行哦~

題目中有說(shuō)明字符串長(zhǎng)度最大為5000，但是dp數(shù)組開(kāi)到 5000?5000$5000*5000$ 的話會(huì)內(nèi)存超限。

有兩種解決方案：

AC 代碼