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()
Sl = S[:N]
Sr = S[N:]

from collections import defaultdict
L = defaultdict(int)
R = defaultdict(int)
for i in range(1<<N):
    t1 = ""
    t2 = ""
    for j in range(N):
        if i & (1<<j):
            t1 += Sl[j]
    for j in range(N-1, -1, -1):
        if not i & (1<<j):
            t2 += Sl[j]
    L[(t1, t2)] += 1
    t1 = ""
    t2 = ""
    for j in range(N-1, -1, -1):
        if i & (1<<j):
            t1 += Sr[j]
    for j in range(N):
        if not i & (1<<j):
            t2 += Sr[j]
    R[(t1, t2)] += 1
ans = 0
for k, v in L.items():
    ans += R[k] * v
print(ans)