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
'''input
1 
0 

0 

1 

0 

'''

 
import sys
from bisect import bisect_left as bl
from itertools import permutations as p
from collections import defaultdict as df

n=input()
A=[]
A+=p(list(range(4)))
Sq=[]
for i in range(4):
    sq=[]
    for i in range(n):
        sq.append(list(raw_input().strip()))
    Sq.append(sq)
    try:
        raw_input()
    except:
        pass
   


def check(board):
    m1=0
    m2=0
    do="01"
    for i in range(len(board)):
        for j in range(len(board)):
            if do[(i+j)&1]!=board[i][j]:
                m1+=1
            else:
                m2+=1
    return min(m1,m2)
ans=99999999
for perm in A:
    newboard=[]
    for i in range(n*2):
        newboard.append(['0']*(2*n))

    for k in range(4):
        for i in range(n):
            for j in range(n):
                newboard[ (k/2)*n+i][(k%2)*n+j]=Sq[perm[k]][i][j]

    ans=min(ans,check(newboard))
    #print newboard
    #print check(newboard)
print ans
