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
"""Codeforces P961C. Chessboard Sleep
    (http://codeforces.com/problemset/problem/961/C)

Problem tags: bitmasks, brute force

Time Complexity: O(n^2)
"""

########################################
# Common code for IO buffering
########################################
import atexit
import io
import sys

_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())


########################################
# Main code
########################################
import itertools

def main():
    n = int(input())
    segments = []
    for _ in range(3):
        segments.append([input() for x in range(n)])
        input()
    segments.append([input() for x in range(n)])    
    
    diffs = []
    for seg in segments:
        diff = 0
        for i in range(n):
            for j in range(n):
                if int(seg[i][j]) == (i + j) % 2:
                    diff += 1
        diffs.append(diff)
    diff_sum = sum(diffs)

    print(
        min(diff_sum - a - b + (n * n - a) + (n * n - b)
            for a, b
            in itertools.combinations(diffs, 2)))
  
    
if __name__ == '__main__':
    main()
