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
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")


n = int(input())
s = input()
t = s[-1:-n-1:-1]
def sub(r,b):
    # tを分割してr,bを作る通り数
    dp = [[0]*(len(b)+1) for _ in range(len(r)+1)]
    dp[0][0] = 1
    for i in range(len(r)+1):
        for j in range(len(b)+1):
#             if i+j>=n:
#                 continue
            if i<len(r) and t[i+j]==r[i]:
                dp[i+1][j] += dp[i][j]
            if j<len(b) and t[i+j]==b[j]:
                dp[i][j+1] += dp[i][j]
    return dp[len(r)][len(b)]


ans = 0
for bit in range(1<<n):
    r = []
    b = []
    for i in range(n):
        if bit>>i&1:
            r.append(s[i])
        else:
            b.append(s[i])
    ans += sub(r,b)
print(ans)