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
import sys
def input(): return sys.stdin.readline().rstrip()
def I(): return int(input())
def S(): return input()
# ----------------------------------------------------------- #

n = I()
s = S()
sa = s[:n]
sb = s[n:][::-1]

A = defaultdict(int)
B = defaultdict(int)

for bit in range(1<<n):
    red_A = []
    red_B = []
    blue_A = []
    blue_B = []
    for i in range(n):
        if bit & 1<<i:
            red_A.append(sa[i])
            blue_B.append(sb[i])
        else:
            blue_A.append(sa[i])
            red_B.append(sb[i])
    a_key = (''.join(red_A), ''.join(blue_A))
    b_key = (''.join(blue_B), ''.join(red_B))
    A[a_key] += 1
    B[b_key] += 1

ans = 0
for key in A.keys():
    if key in B:
        ans += A[key]*B[key]

print(ans)