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
printn = lambda x: print(x,end='')
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
ins = lambda : input().strip()
DBG = True # and False
BIG = 10**18
R = 10**9 + 7
#R = 998244353

def ddprint(x):
  if DBG:
    print(x)

n = inn()
s = ins()
l = s[:n]
r = s[n:]
r = r[::-1]
h = defaultdict(int)
for i in range(2**n):
    x = ""
    y = ""
    for j in range(n):
        if (i>>j)%2==0:
            x += l[j]
        else:
            y += l[j]
    h[(x,y)] += 1
ans = 0
for i in range(2**n):
    x = ""
    y = ""
    for j in range(n):
        if (i>>j)%2==0:
            x += r[j]
        else:
            y += r[j]
    if (x,y) in h:
        #ddprint(f"{x=} {y=} h {h[(x,y)]}")
        ans += h[(x,y)]
print(ans)