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 Counter
N = int(input())
S = input()
ctr1 = Counter()
ctr2 = Counter()

for b in range(2**N):
    blue = red = ''
    for k in range(N):
        if b & (1<<k):
            blue += S[k]
        else:
            red += S[k]
    ctr1[(blue,red)] += 1

T = S[::-1][:N]
for b in range(2**N):
    blue = red = ''
    for k in range(N):
        if b & (1<<k):
            blue += T[k]
        else:
            red += T[k]
    ctr2[(blue,red)] += 1

ans = 0
for (b1,r1),v1 in ctr1.items():
    ans += v1 * ctr2[(r1,b1)]
print(ans)