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:
# C
N = int(input())
S = list(input())
S1 = S[:N]
S2 = S[2*N-1:N-1:-1]

dict_1 = dict()
q_list = [""]*(2**N)
res = 0

for i in range(2**N):
    sb = bin(2**N+i)[3:]
    red = []
    blue = []
    red2 = []
    blue2 = []
    for j in range(N):
        if sb[j]=="0":
            red.append(S1[j])
            red2.append(S2[j])
        else:
            blue.append(S1[j])
            blue2.append(S2[j])
    sss = "".join(red+["|"]+blue)
    sss2 = "".join(red2+["|"]+blue2)
    if sss not in dict_1.keys():
        dict_1[sss] = 1
    else:
        dict_1[sss] += 1
    q_list[i] = sss2
for q in q_list:
    res += dict_1.get(q, 0)
print(res)