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
n = int(input())

pieces = []
recolors = []
for i in range(4):
    piece = []
    for j in range(n):
        line = input().strip()
        piece.append(line)
    if i != 3:
        input()
    pieces.append(piece)
    cur1 = 0
    for x in range(n):
        for y in range(n):
            cur1 += (x + y + int(piece[x][y])) % 2
    cur2 = 0
    for x in range(n):
        for y in range(n):
            cur2 += (x + y + 1 + int(piece[x][y])) % 2
    recolors.append([cur1, cur2])

#print(recolors)

mmin = (2 * n) * (2 * n)
enums = [[[0, 1], [2, 3]],
         [[0, 2], [1, 3]],
         [[0, 3], [1, 2]],
         [[1, 2], [0, 3]],
         [[1, 3], [0, 2]],
         [[2, 3], [0, 1]]]
for i in range(len(enums)):
    a, b = enums[i]
    #print(a, b, recolors)
    summ = recolors[a[0]][0] + recolors[a[1]][0] + recolors[b[0]][1] + recolors[b[1]][1]
    mmin = min((mmin, summ))
print(mmin)
  	 						  	 	  	 		  	  	 	