Problem: 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.

Constraints

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

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.

Examples

Input

4
cabaacba


Output

4


Input

11
mippiisssisssiipsspiim


Output

504


Input

4
abcdefgh


Output

0


Input

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


Output

9075135300

Solution (in PYTHON3):

Solution:
from collections import defaultdict

N = int(input())
S = input()
left = S[:N]
right = S[:N-1:-1]

# leftの(blue, red)のパターンを全列挙
br_pattern = defaultdict(int)

for bit in range(1<<N):
    blue = ""
    red = ""
    for isb in range(N):
        if bit & (1<<isb):
            blue = blue + left[isb]
        else:
            red = red + left[isb]
            
    br_pattern[(blue, red)] += 1

# rightの(red, blue)のパターンをひとつずつ調べ、br_patternに一致する数だけansに足す
ans = 0
for bit in range(1<<N):
    red = ""
    blue = ""
    for isr in range(N):
        if bit & (1<<isr):
            red = red + right[isr]
        else:
            blue = blue + right[isr]
            
    ans += br_pattern[(red, blue)]
        
print(ans)