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:
N=int(input())
s=input()

sa=s[:N]
sb=s[N:]

import itertools
ALLIST=list(itertools.product((0,1),repeat=N))

from collections import defaultdict
STRA = defaultdict(int)
STRB = defaultdict(int)

for i in ALLIST:
    red_a=""
    blue_a=""
    red_b=""
    blue_b=""
    for j in range(N):
        if i[j]==0:
            red_a+=sa[j]
            red_b+=sb[j]
        else:
            blue_a+=sa[j]
            blue_b+=sb[j]

    STRA[(red_a[::-1],blue_a[::-1])]+=1
    STRB[(red_b,blue_b)]+=1

ANS=0
for key in STRA:
    ANS+=STRA[key]*STRB[key]

print(ANS)