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 __future__ import print_function
n= int(raw_input())
pra = [[(i + j) % 2 for i in range(2 * n) ] for j in range(2 * n) ]
prb = [[(i + j + 1) % 2 for i in range(2 * n) ] for j in range(2 * n) ]
rres = 1000000000
bl = []
for i in range(4):
    tbl = []
    for j in range(n):
        tbl.append(list(map(int,list(raw_input()))))
    bl.append(tbl)
    if i != 3:
        raw_input()
for i1 in range(4):
    for i2 in range(4):
        for i3 in range(4):
            for i4 in range(4):
                if len(set([i1,i2,i3,i4])) != 4:
                    continue
                res = 0
                for i in range(2 * n):
                    for j in range(2 * n):
                        if i < n and j < n:
                            res += not(pra[i][j] == bl[i1][i][j])
                        elif i < n:
                            res += not(pra[i][j] == bl[i2][i][j - n])
                        elif j < n:
                            res += not(pra[i][j] == bl[i3][i - n][j])
                        else:
                            res += not(pra[i][j] == bl[i4][i - n][j - n])
                rres = min(res,rres)

                res = 0
                for i in range(2 * n):
                    for j in range(2 * n):
                        if i < n and j < n:
                            res += not(prb[i][j] == bl[i1][i][j])
                        elif i < n:
                            res += not(prb[i][j] == bl[i2][i][j - n])
                        elif j < n:
                            res += not(prb[i][j] == bl[i3][i - n][j])
                        else:
                            res += not(prb[i][j] == bl[i4][i - n][j - n])
                rres = min(res,rres)
print(rres)