Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. 

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. 

Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.

Examples

Input

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
from sys import stdin
take=lambda: map(int,stdin.readline().split())
from itertools import combinations

def one(n,arr):
    one=['1','0']*(n/2) +['1']
    zero=['0','1']*(n/2)+['0']
    req=[one,zero]*(n/2)+[one]
    c=0
    for i in range(n):
        for j in range(n):
            if arr[i][j]!=req[i][j]:
                c+=1

    return c


def zero(n,arr):
    one = ['1', '0'] * (n / 2) + ['1']
    zero = ['0', '1'] * (n / 2) + ['0']
    req = [zero,one] * (n / 2) + [zero]
    c = 0
    for i in range(n):
        for j in range(n):
            if arr[i][j] != req[i][j]:
                c += 1
    return c


n=input()
a=[]
b=[]
arr=[]
for i in range(n):
    arr.append(list(stdin.readline()))
a.append(one(n,arr))
b.append(zero(n,arr))
g=list(stdin.readline())
arr=[]
for i in range(n):
    arr.append(list(stdin.readline()))
a.append(one(n, arr))
b.append(zero(n, arr))
g=list(stdin.readline())
arr=[]
for i in range(n):
    arr.append(list(stdin.readline()))
a.append(one(n, arr))
b.append(zero(n, arr))
g=list(stdin.readline())
arr=[]
for i in range(n):
    arr.append(list(stdin.readline()))
a.append(one(n, arr))
b.append(zero(n, arr))
com=combinations([0,1,2,3],2)
g=list(stdin.readline())
ans=10**10
for h in com:
    i,j=h
    p=[]
    for v in range(4):
        if v not in [i,j]:
            p.append(v)
    x,y=p
    #print i,j,x,y
    ans=min(ans,a[i]+a[j]+b[x]+b[y])
print ans





