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
import sys
import math

def diff(grid,grid1,grid2):
    d1 = d2 = 0
    for i in range(n):
        for j in range(n):
            if grid[i][j] != grid1[i][j]:
                d1 += 1
            if grid[i][j] != grid2[i][j]:
                d2 += 1
    return d1,d2

def sol(i,p1,p2):
    if i == 4:
        if p1 == p2:
            return 0
        return float('inf')
    return min(d1s[i] + sol(i+1,p1+1,p2), d2s[i] + sol(i+1,p1,p2+1))


n = int(sys.stdin.readline().strip())

row1 = []
row2 = []
for i in range(n):
    if i%2:
        row1.append('1')
        row2.append('0')
    else:
        row1.append('0')
        row2.append('1')
row1 = ''.join(row1)
row2 = ''.join(row2)

grid1 = []
grid2 = []

for i in range(n):
    if i%2:
        grid1.append(row1)
        grid2.append(row2)
    else:
        grid1.append(row2)
        grid2.append(row1)

pieces = [0,0]
d1s = []
d2s = []

for i in range(4):
    grid = []
    prec = 0
    for j in range(n):
        grid.append(sys.stdin.readline().strip())
    _ = sys.stdin.readline()

    d1, d2 = diff(grid, grid1, grid2)

    if d1 == 0:
        pieces[0] += 1
    elif d2 == 0:
        pieces[1] += 1
    d1s.append(d1)
    d2s.append(d2)

print(sol(0,0,0))
