Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

4
cabaacba

Sample Output 1

4

There are four ways to paint the string, as follows:

cabaacba

cabaacba

cabaacba

cabaacba

Sample Input 2

11
mippiisssisssiipsspiim

Sample Output 2

504

Sample Input 3

4
abcdefgh

Sample Output 3

0

Sample Input 4

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 4

9075135300

The answer may not be representable as a 32-bit integer.

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import defaultdict, deque, Counter
from heapq import heappush, heappop, heapify
from itertools import permutations, accumulate, combinations, combinations_with_replacement
from math import sqrt, ceil, floor, factorial
from bisect import bisect_left, bisect_right, insort_left, insort_right
from copy import deepcopy
from operator import itemgetter
from functools import reduce, lru_cache  # @lru_cache(None)
from fractions import gcd
import sys
def input(): return sys.stdin.readline().rstrip()
def I(): return int(input())
def Is(): return (int(x) for x in input().split())
def LI(): return list(Is())
def TI(): return tuple(Is())
def IR(n): return [I() for _ in range(n)]
def LIR(n): return [LI() for _ in range(n)]
def TIR(n): return [TI() for _ in range(n)]
def S(): return input()
def Ss(): return input().split()
def LS(): return list(S())
def SR(n): return [S() for _ in range(n)]
def SsR(n): return [Ss() for _ in range(n)]
def LSR(n): return [LS() for _ in range(n)]
sys.setrecursionlimit(10**6)
MOD = 10**9+7
INF = 10**18
# ----------------------------------------------------------- #

n = I()
s = S()
sa = s[:n]
sb = s[n:][::-1]

A = defaultdict(int)
B = defaultdict(int)

for bit in range(1<<n):
    red_A = ""
    red_B = ""
    blue_A = ""
    blue_B = ""
    for i in range(n):
        if bit & 1<<i:
            red_A += sa[i]
            blue_B += sb[i]
        else:
            blue_A += sa[i]
            red_B += sb[i]
    A[(red_A, blue_A)] += 1
    B[(blue_B, red_B)] += 1

ans = 0
for key in A.keys():
    if key in B.keys():
        ans += A[key]*B[key]

print(ans)