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()
first = S[:N]
latter = S[N:][::-1]

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

ans = 0
for i in range(2**N):
    pattern = list(format(i,digit))
    red = []
    blue = []
    for j in range(N):
        if pattern[j] == "1":
            red.append(latter[j])
        else:
            blue.append(latter[j])
    key = ",".join(("".join(red),"".join(blue)))
    if key in dic:
        ans += dic[key]

print(ans)