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

def main():
    n = int(input())
    cb0 = [list(map(int, input())) for _ in range(n)]
    _ = input()
    cb1 = [list(map(int, input())) for _ in range(n)]
    _ = input()
    cb2 = [list(map(int, input())) for _ in range(n)]
    _ = input()
    cb3 = [list(map(int, input())) for _ in range(n)]
    print(solve(n, [cb0, cb1, cb2, cb3]))

def solve(n, cbs):
    return min(cost(n, p) for p in permutations(cbs))

def cost(n, p):
    # print(p)
    n2 = 2 * n
    p2 = [p[:2], p[2:]]
    cost1 = sum(1 for i in range(n2) for j in range(n2) if p2[i//n][j//n][i%n][j%n] == (i+j) % 2)
    cost2 = sum(1 for i in range(n2) for j in range(n2) if p2[i//n][j//n][i%n][j%n] == (i+j+1) % 2)
    return min(cost1, cost2)

main()
