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Problem A
Making Palindromes
An alphabetical string is a string consisting of $0$ or more capital letters (i.e. [‘A’..‘Z’]). Given an alphabetical string $S[1..N]$, determine the number of palindromic alphabetical strings of length $2N$ that contains $S$ as a subsequence (not necessarily contiguous). A string is palindromic if it is equal to its reverse.
Input
The first line of input is an integer representing $N$, constrained to $0 \leq N \leq 200$.
The second line of input is an alphabetical string $S$ of length $N$.
Output
Output the number of palindromic alphabetical strings of length $2N$ containing $S$ as a subsequence. As this could be rather large, output it modulo $10^9+7$.
| Sample Input 1 | Sample Output 1 |
|---|---|
2 AA |
51 |
| Sample Input 2 | Sample Output 2 |
|---|---|
2 AB |
2 |
