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 itertools import product, compress
from collections import Counter

N = int(input())
Ss = input()

S1s = Ss[:N]
ptn1s = [''.join(compress(S1s, sels)) for sels in product(range(2), repeat=N)]
cnt1 = Counter([(red, blue) for red, blue in zip(ptn1s, reversed(ptn1s))])

S2s = Ss[N:][::-1]
ptn2s = [''.join(compress(S2s, sels)) for sels in product(range(2), repeat=N)]
cnt2 = Counter([(red, blue) for red, blue in zip(ptn2s, reversed(ptn2s))])

ans = 0
for ptn1, num1 in cnt1.items():
    ans += num1 * cnt2[ptn1]
print(ans)