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())
need = []
smth = []
for i in range(n):
    s = ''
    for j in range(n):
        if i % 2 == 0:
            if j % 2 == 0:
                s += '1'
            else:
                s += '0'
        else:
            if j % 2 == 1:
                s += '1'
            else:
                s += '0'
    smth.append(s)
need.append(smth)
smth = []
for i in range(n):
    s = ''
    for j in range(n):
        if i % 2 == 0:
            if j % 2 == 0:
                s += '0'
            else:
                s += '1'
        else:
            if j % 2 == 1:
                s += '0'
            else:
                s += '1'
    smth.append(s)
need.append(smth)
kolvo = []
for i in range(4):
    a = []
    now = []
    sum1 = 0
    sum2 = 0
    for j in range(n):
        s = input()
        now.append(s)
    for x in range(len(now)):
        for y in range(len(now[x])):
            if x % 2 == 0:
                if y % 2 == 0 and now[x][y] == '0':
                    sum1 += 1
                elif y % 2 == 1 and now[x][y] == '1':
                    sum1 += 1
            else:
                if y % 2 == 0 and now[x][y] == '1':
                    sum1 += 1
                elif y % 2 == 1 and now[x][y] == '0':
                    sum1 += 1
    a.append(sum1)
    for x in range(len(now)):
        for y in range(len(now[x])):
            if x % 2 == 0:
                if y % 2 == 0 and now[x][y] == '1':
                    sum2 += 1
                elif y % 2 == 1 and now[x][y] == '0':
                    sum2 += 1
            else:
                if y % 2 == 0 and now[x][y] == '0':
                    sum2 += 1
                elif y % 2 == 1 and now[x][y] == '1':
                        sum2 += 1
    a.append(sum2)
    kolvo.append(a)
    if i != 3:
        s = input()
ans = 10000000000000000000000000000000000000000000000000000000000000000
for i in range(len(kolvo) - 1):
    for j in range(i + 1, len(kolvo)):
        ind = []
        for z in range(len(kolvo)):
            if z != i and z != j:
                ind.append(z)
        x = ind[0]
        y = ind[1]
        if kolvo[i][0] + kolvo[j][0] + kolvo[x][1] + kolvo[y][1] < ans:
            ans = kolvo[i][0] + kolvo[j][0] + kolvo[x][1] + kolvo[y][1]
for i in range(len(kolvo) - 1):
    for j in range(i + 1, len(kolvo)):
        ind = []
        for z in range(len(kolvo)):
            if z != i and z != j:
                ind.append(z)
        x = ind[0]
        y = ind[1]
        if kolvo[i][1] + kolvo[j][1] + kolvo[x][0] + kolvo[y][0] < ans:
            ans = kolvo[i][1] + kolvo[j][1] + kolvo[x][0] + kolvo[y][0]
print(ans)
        