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
n=int(input())
aa=[0]*4
for i in range(4):
   aa[i]=''.join(input() for j in range(n))
   if(i!=3):
      input()

x=''.join('10' for i in range((n**2)//2)) +'1'
y=''.join('01' for i in range((n**2)//2)) +'0'
#print(aa,x,y)
x=int(x,2)
y=int(y,2)

#print(a,b,c,d,x,y)
a=[0]*4
b=[0]*4
for i in range(4):
   a[i]=bin(x^int(aa[i],2))[2:].count('1')
   b[i]=bin(y^int(aa[i],2))[2:].count('1')
#print(ch1,ch2)

ans=[a[0]+a[1]+ b[2]+b[3],  a[0]+a[2]+ b[1]+b[3],  a[0]+a[3]+ b[2]+b[1],  a[1]+a[2]+ b[0]+b[3],  a[1]+a[3]+ b[0]+b[2],  a[2]+a[3]+ b[0]+b[1],  ]
      
print(min(ans))
