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 defaultdict

N = int(input())
S = input()

S1 = S[:N]
S2 = S[N:][::-1]
D = defaultdict(int)
ans = 0

for i in range(2**N):
    bit = bin(2**N+i)[3:]
    red1 = "".join([d for d, s in zip(S1, bit) if s == "1"])
    blue1 = "".join([d for d, s in zip(S1, bit) if s == "0"])
    D[(red1, blue1)] += 1

for i in range(2 ** N):
    bit = bin(2 ** N + i)[3:]
    red2 = "".join([d for d, s in zip(S2, bit) if s == "1"])
    blue2 = "".join([d for d, s in zip(S2, bit) if s == "0"])
    ans += D[(blue2, red2)]

print(ans)