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 collections, math

local = False
if local:
    file = open("inputt.txt", "r")

def inp():
    if local:
        return file.readline().rstrip()
    else:
        return input().rstrip()

def ints():
    return [int(_) for _ in inp().split()]


n = int(inp())

k = [[] for _ in range(4)]

for i in range(4):
    grid = ["" for _ in range(n)]

    for _ in range(n):
        grid[_] = inp()

    if i<3:
        inp()

    k[i] = grid

goBlackCrossCount = [0]*4

for i in range(4):
    grid = k[i]

    for r in range(n):
        for c in range(n):
            if r%2==0:
                if c%2==0:
                    if grid[r][c]=="1":
                        goBlackCrossCount[i] += 1
                else:
                    if grid[r][c]=="0":
                        goBlackCrossCount[i] += 1
            else:
                if c%2==0:
                    if grid[r][c]=="0":
                        goBlackCrossCount[i] += 1
                else:
                    if grid[r][c]=="1":
                        goBlackCrossCount[i] += 1

goBlackCrossCount.sort()
ans = goBlackCrossCount[0]+goBlackCrossCount[1]+(n**2)-goBlackCrossCount[2]+(n**2)-goBlackCrossCount[3]

print(ans)
    



