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
"""
1
0

0

1

0
"""

import sys

n = int(input())


def read_board(n, numb):
    board = []
    for i in range(n):
        line = input()
        board.append([int(c) for c in line])
    # board = [[int(c) for c in input().strip()] for i in range(n)]
    if numb != 3:
        input()
    return board

boards = [read_board(n, i) for i in range(4)]
# a = [[1, 0, 1], [0, 0, 0], [0, 0, 1]]
# print(boards)
def _calc_line(l, start=1):
    cur = start
    errors = 0
    for cell in l:
        errors += cell != cur
        cur = not cur
    return errors

def _calc_board(b, start=1):
    errors = 0
    cur = start
    for line in b:
        errors += _calc_line(line, cur)
        cur = not cur
    return errors

checks = [
    (0, 0, 1, 1),
    (0, 1, 0, 1),
    (1, 0, 0, 1),
    (0, 1, 1, 0),
    (1, 0, 1, 0),
    (1, 1, 0, 0)
]

def check_all(boards):
    for check in checks:
        errs = 0
        for board, start in zip(boards, check):
            errs += _calc_board(board, start)
        yield errs

print(min(check_all(boards)))

