Buggy python submission (verdict: Time Limit Exceeded):
from collections import defaultdict
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.append(sa[i])
            blue_B.append(sb[i])
        else:
            blue_A.append(sa[i])
            red_B.append(sb[i])
    a_key = (''.join(red_A), ''.join(blue_A))
    b_key = (''.join(blue_B), ''.join(red_B))
    A[a_key] += 1
    B[b_key] += 1

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

print(ans)


Fixed submission:
from collections import defaultdict
import sys
def input(): return sys.stdin.readline().rstrip()
def I(): return int(input())
def S(): return input()
# ----------------------------------------------------------- #

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.append(sa[i])
            blue_B.append(sb[i])
        else:
            blue_A.append(sa[i])
            red_B.append(sb[i])
    a_key = ''.join(red_A) + ',' + ''.join(blue_A)
    b_key = ''.join(blue_B) + ',' + ''.join(red_B)
    A[a_key] += 1
    B[b_key] += 1

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

print(ans)

Buggy python submission (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)


Fixed submission:
from collections import defaultdict
import sys
def input(): return sys.stdin.readline().rstrip()
def I(): return int(input())
def S(): return input()
# ----------------------------------------------------------- #

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.append(sa[i])
            blue_B.append(sb[i])
        else:
            blue_A.append(sa[i])
            red_B.append(sb[i])
    a_key = ''.join(red_A) + ',' + ''.join(blue_A)
    b_key = ''.join(blue_B) + ',' + ''.join(red_B)
    A[a_key] += 1
    B[b_key] += 1

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

print(ans)

Buggy python submission (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)


Fixed submission:
from collections import defaultdict
import sys
def input(): return sys.stdin.readline().rstrip()
def I(): return int(input())
def S(): return input()
# ----------------------------------------------------------- #

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.append(sa[i])
            blue_B.append(sb[i])
        else:
            blue_A.append(sa[i])
            red_B.append(sb[i])
    a_key = ''.join(red_A) + ',' + ''.join(blue_A)
    b_key = ''.join(blue_B) + ',' + ''.join(red_B)
    A[a_key] += 1
    B[b_key] += 1

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

print(ans)