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

def I(): return int(sys.stdin.readline().rstrip())
def LS2(): return list(sys.stdin.readline().rstrip())  #空白なし

N = I()
S = LS2()

# 左N個のマスをどう塗るかで半分全列挙

ans = 0
left = []
right = []
for i in range(2**N):
    red = []
    blue = []
    for j in range(N):
        if (i >> j) & 1:
            red.append(S[j])
        else:
            blue.append(S[j])
    red = ''.join(red)
    blue = ''.join(blue)
    left.append((red,blue))
for i in range(2**N):
    red = []
    blue = []
    for j in range(N):
        if (i >> j) & 1:
            red.append(S[j+N])
        else:
            blue.append(S[j+N])
    red,blue = blue,red
    red.reverse()
    blue.reverse()
    red = ''.join(red)
    blue = ''.join(blue)
    right.append((red,blue))

from operator import itemgetter

right = sorted(right,key = itemgetter(0,1))

from bisect import bisect_left,bisect

ans = 0
for i in range(2**N):
    ans += bisect(right,left[i]) - bisect_left(right,left[i])

print(ans)