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 = input()
S1 = S[:N]
S2 = S[N::][::-1]
H = dict()
for i in range(2**N):
    t1 = ''.join([s for j, s in enumerate(S2) if 2**j & i])
    t2 = ''.join([s for j, s in enumerate(S2) if not 2**j & i])
    k = H.get((t1, t2), 0)
    H[(t1, t2)] = k+1
ans = 0
for i in range(2**N):
    t1 = ''.join([s for j, s in enumerate(S1) if 2**j & i])
    t2 = ''.join([s for j, s in enumerate(S1) if not 2**j & i])
    ans += H.get((t1, t2), 0)
print(ans)