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 = list(input())
l = s[:n]
r = list(reversed(s[n:]))
hashl = {}
hashr = {}
for i in range(1 << n):
    llr = []
    llb = []
    lrr = []
    lrb = []
    for k in range(n):
        if i & (1 << k):
            llr.append(l[k])
            lrr.append(r[k])
        else:
            llb.append(l[k])
            lrb.append(r[k])
    sl = (''.join(llr), ''.join(llb))
    sr = (''.join(lrr), ''.join(lrb))

    if sl not in hashl: hashl[sl] = 1
    else: hashl[sl] += 1
    if sr not in hashr: hashr[sr] = 1
    else: hashr[sr] += 1
ret = 0
for strpair, c in hashl.items():
    if strpair in hashr:
        ret += hashr[strpair] * c
print(ret)