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 itertools import permutations

n = int(input())

boards = []
for i in range(4):
    board = [input() for j in range(n)]
    boards.append(board)
    if i != 3:
        input()

perms = list(permutations(list(range(4))))


def cost(board):

    base1 = [1,0]*(len(board)//2)
    base2 = [0,1]*(len(board)//2)

    board1 = []
    board2 = []
    for i in range(len(board)//2):
        board1.append(base1)
        board1.append(base2)

        board2.append(base2)
        board2.append(base1)

    board = [list(map(int, list(a))) for a in board]

    curr_min_cost1 = 0
    curr_min_cost2 = 0
    for i in range(len(board)):
        for j in range(len(board)):
            curr_min_cost1 += board[i][j] ^ board1[i][j]
            curr_min_cost2 += board[i][j] ^ board2[i][j]

    return min(curr_min_cost1, curr_min_cost2)


min_cost = float('inf')
for p in perms:
    b1 = boards[p[0]]+boards[p[1]]
    b2 = boards[p[2]]+boards[p[3]]
    b = [a+b for a,b in zip(b1, b2)]
    min_cost = min(min_cost, cost(b))

print(min_cost)
