Buggy python submission (verdict: Time Limit Exceeded):
import itertools
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    L[(T0,T1)]=L.get((T0,T1),0)+1
    R[(T2,T3)]=R.get((T2,T3),0)+1
for tup in L:
    ans+=L[tup]*R.get(tup,0)
print(ans)


Fixed submission:
import itertools
import bisect
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    if (T0,T1) in L:
        L[(T0,T1)]+=1
    else:
        L[(T0,T1)]=1
    if (T2,T3) in R:
        R[(T2,T3)]+=1
    else:
        R[(T2,T3)]=1
for tup in L:
    if tup in R:
        ans+=L[tup]*R[tup]
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    L[(T0,T1)]=L.get((T0,T1),0)+1
    R[(T2,T3)]=R.get((T2,T3),0)+1
for tup in L:
    if tup in R:
        ans+=L[tup]*R[tup]
print(ans)


Fixed submission:
import itertools
import bisect
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    if (T0,T1) in L:
        L[(T0,T1)]+=1
    else:
        L[(T0,T1)]=1
    if (T2,T3) in R:
        R[(T2,T3)]+=1
    else:
        R[(T2,T3)]=1
for tup in L:
    if tup in R:
        ans+=L[tup]*R[tup]
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import itertools
import queue
N=int(input())
S=input()
ans=0
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    for i in range(N):
        if seq[i]==0:
            T0=T0+S[i]
        else:
            T1=T1+S[i]
        T2+=S[-i-1]
    q=[queue.Queue() for i in range(N+1)]
    q[0].put((0,0))
    a0=len(T0)
    a1=len(T1)
    #print(T0,T1,T2)
    for i in range(N):
        while(not(q[i].empty())):
            r=q[i].get()
            #print(i,r)
            #print(r)
            if r[0]+r[1]>=N:
                continue
            if r[0]>=a0:
                if T2[r[1]+r[0]]==T1[r[1]]:
                    q[i+1].put((r[0],r[1]+1))
            elif r[1]>=a1:
                if T2[r[1]+r[0]]==T0[r[0]]:
                    q[i+1].put((r[0]+1,r[1]))
            else:
                if T2[r[1]+r[0]]==T0[r[0]]:
                    q[i+1].put((r[0]+1,r[1]))
                if T2[r[1]+r[0]]==T1[r[1]]:
                    q[i+1].put((r[0],r[1]+1))
    while(not(q[N].empty())):
        r=q[N].get()
        #print(N,r)
        ans+=1
        #print(ans)
print(ans)


Fixed submission:
import itertools
import bisect
N=int(input())
S=input()
ans=0
L=dict()
R=dict()
for seq in itertools.product([0,1],repeat=N):
    T0=""
    T1=""
    T2=""
    T3=""
    for i in range(N):
        if seq[i]==0:
            T0+=S[i]
            T2+=S[-i-1]
        else:
            T1+=S[i]
            T3+=S[-i-1]
    a0=len(T0)
    a1=len(T1)
    a2=len(T2)
    a3=len(T3)
    if (T0,T1) in L:
        L[(T0,T1)]+=1
    else:
        L[(T0,T1)]=1
    if (T2,T3) in R:
        R[(T2,T3)]+=1
    else:
        R[(T2,T3)]=1
for tup in L:
    if tup in R:
        ans+=L[tup]*R[tup]
print(ans)