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 as perm
import sys
range = xrange
input = raw_input

n = int(input())
C = [c for line in sys.stdin for c in line if c=='0' or c=='1']

B = []
for i in range(4):
    B.append(C[n*n*i:(i+1)*n*n])

opp = {'0':'1','1':'0'}

besta = 100000000000000
for P in perm([0,1,2,3]):
    for I in '01':
        cost = 0
        for i in range(n*n):
            if i%2==0:
                goal = I
            else:
                goal = opp[I]
            if B[P[0]][i]!=goal:
                cost+=1
        for i in range(n*n):
            if i%2==0:
                goal = I
            else:
                goal = opp[I]
            if B[P[1]][i]!=goal:
                cost+=1
        for i in range(n*n):
            if i%2==1:
                goal = I
            else:
                goal = opp[I]
            if B[P[2]][i]!=goal:
                cost+=1
        for i in range(n*n):
            if i%2==1:
                goal = I
            else:
                goal = opp[I]
            if B[P[3]][i]!=goal:
                cost+=1
        besta = min(besta,cost)
print(besta)
