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 $10^9+7$.

-----Examples-----
Sample Input:
2
AA
Sample Output:
51

Source: kattis | Difficulty: HARD


Solutions: