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:
import sys
input = sys.stdin.readline

from collections import Counter

N = int(input())
S = input().rstrip()

left = [('','')]
for s in S[:N]:
    left = [(x[0]+s,x[1]) for x in left] + [(x[0],x[1]+s) for x in left]
left = [x+' '+y for x,y in left]
counter_L = Counter(left)

right = [('','')]
for s in S[N:][::-1]:
    right = [(x[0]+s,x[1]) for x in right] + [(x[0],x[1]+s) for x in right]
right = [x+' '+y for x,y in right]

answer = sum(counter_L[s] for s in right)
print(answer)