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:
n = int(input())
s = str(input())

L = s[0:n]
R = s[n:]
R = list(R)
R.reverse()
R = ''.join(R)

DL = {}
for i in range(2**n):
    p = ''
    q = ''
    for j in range(n):
        if (i >> j)&1:
            p += L[j]
        else:
            q += L[j]
    if (p, q) in DL:
        DL[(p, q)] += 1
    else:
        DL[(p, q)] = 1

DR = {}
for i in range(2**n):
    p = ''
    q = ''
    for j in range(n):
        if (i >> j)&1:
            p += R[j]
        else:
            q += R[j]
    if (p, q) in DR:
        DR[(p, q)] += 1
    else:
        DR[(p, q)] = 1

#print(DL)
#print(DR)
ans = 0
for k, v in DL.items():
    if k in DR:
        ans += v*DR[k]
print(ans)