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,queue,math,copy,itertools
from fractions import gcd
sys.setrecursionlimit(10**7)
INF = 10**18
MOD = 10**9 + 7
LI = lambda : [int(x) for x in sys.stdin.readline().split()]
_LI = lambda : [int(x)-1 for x in sys.stdin.readline().split()]
NI = lambda : int(sys.stdin.readline())
N = NI()
S = input()
sr = S[-1:N - 1:-1]
ans = 0
fwd = []
rev = {}
for bit in range(2**N):
    red1 = ''
    blue1 = ''
    red2 = ''
    blue2 = ''
    b = 1
    for i in range(N):
        if b & bit:
            red1 += S[i]
            red2 += sr[i]
        else:
            blue1 += S[i]
            blue2 += sr[i]
        b <<= 1
    fwd.append(red1 + ' ' +  blue1)
    key = blue2 + ' ' + red2
    if key in rev:
        rev[key] += 1
    else:
        rev[key] = 1

for s in fwd:
    if s in rev:
        ans += rev[s]
print (ans)