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
pieces = []
n = int(input())

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

mindiffs = 10**9
preMade = [["0" if x % 2 == 0 else "1" for x in range(2*n)],
           ["0" if x % 2 == 1 else "1" for x in range(2*n)]]
           
for a in permutations("0123", 4):
    indexes = list(map(int, a))
    currentBoard = []
    for i in range(n):
        currentBoard.append(pieces[indexes[0]][i] + pieces[indexes[1]][i])
    for i in range(n):
        currentBoard.append(pieces[indexes[2]][i] + pieces[indexes[3]][i])
    for i in range(2):
        startval = i
        currentDiffs = 0
        for j in range(2*n):
            currentDiffs += bin(int("".join(preMade[startval]), 2) ^ int("".join(currentBoard[j]), 2)).count("1")
            startval = (startval + 1) % 2    
        mindiffs = min(mindiffs, currentDiffs)

print(mindiffs)