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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-


n = int(input())

def Count(s, flags):
    """
    >>> Count('000', 0) # --> '010'
    1
    >>> Count('000', 1) # --> '101'
    2
    """
    a = str(flags)
    b = str(1 - flags)
    c = 0
    for i in range(len(s)):
        if (i%2 and s[i] != b) or (not i%2 and s[i] != a):
            c += 1
    return c

def ReadPieces():
    s0 = s1 = 0
    for i in range(n):
        s = input()
        if not s:
            s = input()
        s0 += Count(s, i%2)
        s1 += Count(s, (i+1)%2)
    return s0, s1

b = []
for i in range(4):
    a0, a1 = ReadPieces()
    b.append([a0, a1])

def f(i, j):
    s = 0
    for k in range(4):
        if k == i or k == j:
            s += b[k][0]
        else:
            s += b[k][1]
    return s

print(min(f(0,1), f(0,2), f(0,3), f(1,2), f(1,3), f(2,3)))
