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:

import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline

n=int(input())
s=input().strip()

memo={}
def getans(a,b,c):
    while a and c and a[0]==c[-1]:
        a=a[1:]
        c=c[:-1]
    if a and c: return 0
    if b=="":
        if a=="" and c=="": return 1
        else: return 0
    key=a+"/"+b+"/"+c
    if key in memo: return memo[key]
    # select first letter
    ans=0
    for i in range(1,len(b)):
        if b[0]==b[i]:
            ans+=getans(a,b[1:i],b[i+1:]+c)
    # don't select first letter
    ans+=getans(a+b[0],b[1:],c)
    memo[key]=ans
    #print(key,ans)
    return ans

print(getans("",s,"")*2)

#print(len(memo))