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 bisect import bisect_left as bl, bisect_right as br, insort
import sys
import heapq
from math import *
from collections import defaultdict as dd, deque
def data(): return sys.stdin.readline().strip()
def mdata(): return map(int, data().split())
#sys.setrecursionlimit(100000)

n=int(data())
s=[[0,0] for i in range(4)]
for i in range(4):
    t=1
    temp=0
    for j in range(n):
        l=input()
        if j==0 and l[0]=='0':
            t=0
        for k in range(n):
            if ((j+k)%2==0 and int(l[k])!=t) or ((j+k)%2==1 and int(l[k])!=1-t):
                temp+=1
    if i!=3:
        input()
    s[i][t]=temp
    s[i][1-t]=n*n-temp
ans=100000000000
for i in range(4):
    for j in range(i+1,4):
        t=s[i][0]+s[j][0]
        for k in range(4):
            if k!=j and k!=i:
                t+=s[k][1]
        ans=min(ans,t)
print(ans)
