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 fractions import gcd
from math import factorial, ceil, sqrt, atan2, log, pi, e, asin,acos, cos, sin
from itertools import *
from fractions import Fraction
import string
import copy
import random
import bisect
from decimal import *
def id_generator(size=20, chars=string.digits):
    return ''.join(random.choice(chars) for _ in range(size))
 
def mp():
    return map(int,str(raw_input()).split())


n=input()
l=[]
for i in range(4):
    s=[]
    for j in range(n):
        z=str(raw_input())
        s+=[z]
    try:
        x=str(raw_input())
    except:
        pass
    l+=[list(s)]
#print l
z=permutations([0,1,2,3])
val=10**9
for i in z:
    a=i[0]
    b=i[1]
    c=i[2]
    d=i[3]
    ans=[]
    new=[]
    for j in range(n):
        new+=[l[a][j]+l[b][j]]
    ans+=new
    new=[]
    for j in range(n):
        new+=[l[c][j]+l[d][j]]
    ans+=new
    #print ans
    pre1=0
    pre2=0
    for i in range(2*n):
        for j in range(2*n):
            if ans[i][j]=='1' and (i+j)%2==0:
                pre2+=1
            elif ans[i][j]=='0' and (i+j)%2==0:
                pre1+=1
            elif ans[i][j]=='1' and (i+j)%2:
                pre1+=1
            elif ans[i][j]=='0' and (i+j)%2:
                pre2+=1            
    val=min(val,pre1,pre2)
print val