Problem Statement

You are given a string S of length 2N consisting of lowercase English letters.
There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

• The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Input

Input is given from Standard Input in the following format:
N
S

Output

Print the number of ways to paint the string that satisfy the condition.

Constraints

• $1 \leq N \leq 18$
• The length of S is 2N.
• S consists of lowercase English letters.

Sample Input 1

4
cabaacba

Sample Output 1

4

There are four ways to paint the string, as follows:

• cabaacba
• cabaacba
• cabaacba
• cabaacba

Sample Input 2

11
mippiisssisssiipsspiim

Sample Output 2

504

Sample Input 3

4
abcdefgh

Sample Output 3

0

Sample Input 4

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 4

9075135300

The answer may not be representable as a 32-bit integer.

见题面 Input 部分

见题面 Output 部分