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())
if n==1:
      d=dict()
      d[0]=0
      d[1]=0
      for i in range(4):
            x=int(input())
            d[x]+=1
            if i<3:
                  vide=input()
      v=list(d.values())
      print(abs(v[0]-2))
else:
      ch1='01'*(n//2)+'0'
      ch2='10'*(n//2)+'1'
      c1=(ch1+ch2)*(n//2)+ch1
      c2=(ch2+ch1)*(n//2)+ch2
      d=dict()
      cas1=0
      cas2=0
      for j in range(4):
            ch=''
            for i in range(n):
                  ch+=input()
            if j<3:
                  vide=input()
            com1=com2=0
            for i in range(len(c1)):
                  if c1[i]== ch[i]:
                        com1+=1
                  else:
                        com2+=1
            if com1>com2:
                  d[(ch,j)]=[1,n**2-com1]
                  cas1+=1
            else:
                  d[(ch,j)]=[2,n**2-com2]
                  cas2+=1
      v=list(d.keys())
      if cas1<cas2:
            while cas1<cas2:
                  m=0
                  p=tuple()
                  for i in v:
                        if d[i][0]==2:
                              if d[i][1]>=m:
                                    m=d[i][1]
                                    p=i
                  d[p]=[1,n**2-m]
                  cas1+=1
                  cas2-=1
      elif cas2<cas1:
            while cas2<cas1:
                  m=0
                  p=tuple()
                  for i in v:
                        if d[i][0]==1:
                              if d[i][1]>=m:
                                    m=d[i][1]
                                    p=i
                  d[p]=[2,n**2-d[p][1]]
                  cas2+=1
                  cas1-=1
      ans=0
      for i in v:
            ans+=d[i][1]
      print(ans)
      
      
