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())


arr = []

def check2(a):
    white = 0
    black = 0
    needwhite = 0
    needblack = 0
    for i in range(len(a)):
        for j in range(len(a[0])):
            if(i+j)% 2 == 0 and a[i][j] == '0':
                white += 1
            elif (i+j)%2 == 0 and a[i][j] == '1':
                needwhite += 1
            elif (i+j)%2 == 1 and a[i][j] == '1':
                black += 1
            else:
                needblack += 1
    return min(needwhite + needblack,white+ black)

for i in range(4):
    s = []
    for j in range(n):
        s.append(input())
    if(i != 3):
        k = input()
    arr.append(s)
answer = 100*100*4

def check(can):
    s = []
    for i in range(n):
        s.append(arr[can[0]][i] + arr[can[1]][i])
    for i in range(n):
        s.append(arr[can[2]][i] + arr[can[3]][i])
    return check2(s)




for i1 in range(4):
    for i2 in range(4):
        if i1 != i2:
            for i3 in range(4):
                if i3 != i2 and i3 != i1:
                    for i4 in range(4):
                        if i4 != i3 and i4 != i2 and i4 != i1:
                           answer = min(check([i1,i2,i3,i4]),answer)
print(answer)