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:
#https://atcoder.jp/contests/agc026/submissions/10971924を参考にした

from collections import defaultdict
n = int(input())
s = input()
ls = s[:n:]
rs = s[:n-1:-1]
d = defaultdict(int)

def full_research(sa,r,b,t):
    if t == n:
        d[(r,b)] += 1
        return
    full_research(sa,r+sa[t],b,t+1)
    full_research(sa,r,b+sa[t],t+1)

full_research(ls,"","",0)
dl = d
d = defaultdict(int)
full_research(rs,"","",0)

ans = 0
for dlk,dlv in dl.items():
    ans += dlv*d[dlk]

print(ans)