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:
# coding: utf-8
import sys
from collections import defaultdict

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

# 一番左を赤として2倍、Counter、N文字ずつ選ぶ
# 制約が少ないので全探索も可能
N = ir()
S = sr()
answer = 0
former = S[:N]
latter = S[N:][::-1]

dic_left = defaultdict(int)
for pattern in range(1<<N):
    red = ''; blue = ''
    for i in range(N):
        if pattern>>i & 1:
            red += S[i]
        else:
            blue += S[i]
    key = (red, blue)
    if key in dic_left:
        dic_left[key] += 1
    else:
        dic_left[key] = 1

dic_right = defaultdict(int)
for pattern in range(1<<N):
    red = ''; blue = ''
    for i in range(N):
        if pattern>>i & 1:
            red += latter[i]
        else:
            blue += latter[i]
    key = (red, blue)
    if key in dic_right:
        dic_right[key] += 1
    else:
        dic_right[key] = 1

answer = 0
for k, v in dic_left.items():
    if k in dic_right:
        answer += v * dic_right[k]

print(answer)
# 解説