Problem I

Again Palindromes

Input: Standard Input

Output: Standard Output

Time Limit: 2 Seconds

A palindorme is a sequence of one or more characters that reads the same from the left as it does from the right. For example, Z, TOT and MADAM are palindromes, but ADAM is not.

Given a sequence S of N capital latin letters. How many ways can one score out a few symbols (maybe 0) that the rest of sequence become a palidrome. Varints that are only  different by an order of scoring out should be considered the same.

Input

The input file contains several test cases (less than 15). The first line contains an integer T that indicates how many test cases are to follow.

Each of the T lines contains a sequence S (1≤N≤60). So actually each of these lines is a test case.

Output

For each test case output in a single line an integer – the number of ways.

Sample Input   

3

BAOBAB

AAAA

ABA

Output for Sample Input

22

15

5

#include <iostream>
#include <string>
#include <cstdio>
#include <cstring>
using namespace std;
const int maxn=65;

string str;
long long dp[maxn][maxn];
int len;

void initial()
{
    for(int i=0; i<maxn; i++)
        for(int j=0; j<maxn; j++)
        {
            if(i==j)  dp[i][j]=1;
            else  dp[i][j]=0;
        }
}

void input()
{
    cin>>str;
    len=str.length();
}

void solve()
{
    for(int i=2; i<=len; i++)
        for(int j=0,k=i-1; k<len; j++,k++)
        {
                dp[j][k]=dp[j+1][k]+dp[j][k-1];
                if(str[j]==str[k])   dp[j][k]+=1;
                else  dp[j][k]-=dp[j+1][k-1];
        }
    printf("%lld\n",dp[0][len-1]);
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        initial();
        input();
        solve();
    }
    return 0;
}