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
from functools import reduce
import math
from decimal import *
def factors(n):
    return set(reduce(list.__add__,
                ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def sol():
    am = int(input())
    pieces = []

    need1 = [0]*4
    need2 = [0]*4

    for i in range(4):
        piece = []
        for g in range(am):
            piece.append(list(map(int,list(input()))))
        for g in range(am):
            for j in range(am):
                need1[i]+= ((piece[g][j] == (j&1==g&1)) + 1)&1
        # for g in range(am):
        #     for j in range(am):
        #         need2[i]+= ((piece[g][j] == (j&1==g&1)))
        if i != 3:
            input()
        pieces.append(piece)
    need1.sort()
    s = 0
    for i in range(2):
        s+=need1[i]
    for i in range(2,4):
        s+= am**2 -need1[i]
    print(s)
    # for i in range(3):
    #     for g in range(3):
    #         print(i&1 == g&1, end=" ")
    #     print('\n')
sol()