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 combinations


def fn(mtrx):
    w = 0
    b = 0
    n = len(mtrx)

    for i in range(n):
        for j in range(n):
            if (i + j) % 2:
                if mtrx[i][j] == '0':
                    w += 1
                else:
                    b += 1
            else:
                if mtrx[i][j] == '1':
                    w += 1
                else:
                    b += 1

    return (w, b)


if __name__ == '__main__':
    n = int(input())

    ms = []

    for i in range(4):
        mtrx = []
        for _ in range(n):
            mtrx.append(list(input()))
        ms.append(mtrx)
        if i < 3:
            input()

    costs = list(map(lambda o: fn(o), ms))
    combs = list(map(lambda o: list(o), combinations(range(4), 2)))

    mc = 40 ** 4

    for ws in combs:
        bs = [0, 1, 2, 3]
        for w in ws:
            bs.remove(w)
        mc = min(mc, costs[ws[0]][0] + costs[ws[1]][0] + costs[bs[0]][1] + costs[bs[1]][1])

    print(mc)
