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 itertools import combinations
N = int(input())
S = list(input())
L = S[:N]
R = S[:2*N][::-1]


digit = "0"+str(N)+"b"
LDic={}
for i in range(2**N):
    pattern = format(i,digit)
    red = []
    blue = []
    for i in range(N):
        if pattern[i] == "1":
            red.append(L[i])
        else:
            blue.append(L[i])
    red = "".join(red)
    blue = "".join(blue)
    key = ",".join([red,blue])
    if key in LDic:
        LDic[key] += 1
    else:
        LDic[key] = 1

RDic={}
for i in range(2**N):
    pattern = format(i,digit)
    red = []
    blue = []
    for i in range(N):
        if pattern[i] == "1":
            red.append(R[i])
        else:
            blue.append(R[i])
    red = "".join(red)
    blue = "".join(blue)
    key = ",".join([blue,red])
    if key in RDic:
        RDic[key] += 1
    else:
        RDic[key] = 1
ans = 0
for k,v in LDic.items():
    if k in RDic:
        ans += v*RDic[k]
print(ans)