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 math import ceil, log

n = int(input())
a1 = []
a2 =[]
a3 = []
a4 = []
for i in range(n):
    a1.append(list(input()))
input()
for i in range(n):
    a2.append(list(input()))
input()
for i in range(n):
    a3.append(list(input()))
input()
for i in range(n):
    a4.append(list(input()))

tmp1 = tmp2 = 0
for i in range(n):
    for j in range(n):
        if (i%2 == 0 and j%2 == 0) or (i%2 == 1 and j%2 == 1):
            if a1[i][j] == "0":
                tmp1+=1
            else:
                tmp2+=1
        else:
            if a1[i][j] == "1":
                tmp1+=1
            else:
                tmp2+=1
cost1 = (tmp1, tmp2)
tmp1 = tmp2 = 0
for i in range(n):
    for j in range(n):
        if (i%2 == 0 and j%2 == 0) or (i%2 == 1 and j%2 == 1):
            if a2[i][j] == "0":
                tmp1+=1
            else:
                tmp2+=1
        else:
            if a2[i][j] == "1":
                tmp1+=1
            else:
                tmp2+=1
cost2 = (tmp1, tmp2)

tmp1 = tmp2 = 0
for i in range(n):
    for j in range(n):
        if (i%2 == 0 and j%2 == 0) or (i%2 == 1 and j%2 == 1):
            if a3[i][j] == "0":
                tmp1+=1
            else:
                tmp2+=1
        else:
            if a3[i][j] == "1":
                tmp1+=1
            else:
                tmp2+=1
cost3 = (tmp1, tmp2)

tmp1 = tmp2 = 0
for i in range(n):
    for j in range(n):
        if (i%2 == 0 and j%2 == 0) or (i%2 == 1 and j%2 == 1):
            if a4[i][j] == "0":
                tmp1+=1
            else:
                tmp2+=1
        else:
            if a4[i][j] == "1":
                tmp1+=1
            else:
                tmp2+=1
cost4 = (tmp1, tmp2)

ans = []
ans.append(cost1[0]+cost2[1]+cost3[1]+cost4[0])
ans.append(cost1[0]+cost3[1]+cost4[1]+cost2[0])
ans.append(cost1[0]+cost3[0]+cost4[1]+cost2[1])
ans.append(cost1[1]+cost2[0]+cost3[0]+cost4[1])
ans.append(cost1[1]+cost3[1]+cost4[0]+cost2[0])
ans.append(cost1[1]+cost3[0]+cost4[0]+cost2[1])
print(min(ans))



