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()

result = 0

S1 = S[:N]
S2 = S[N:][::-1]

def calc(s, x):
    s1 = ""
    s2 = ""
    for c in s:
        if x & 1:
            s1 += c
        else:
            s2 += c
        x >>= 1
    return s1, s2

from collections import defaultdict

kv = defaultdict(int)

for i in range(2**N):
    kv[calc(S2, i)] += 1

for i in range(2**N):
    result += kv[calc(S1, i)]

print(result)