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
import sys
n=int(input())
M=[['0' for k in range(n)]for _ in range(n)]
L=[['0' for k in range(n)]for _ in range(n)]
for i in range(n):
  for j in range(n):
    if j%2==i%2:
      M[i][j]='1'
for i in range(n):
  for j in range(n):
    if j%2!=i%2:
      L[i][j]='1'
def test(K):
  m=0 
  for i in range(n):
    for j in range(n):
      if M[i][j]!=K[i][j]:
        m+=1
  
  return m
A=[]
for _ in range(4):
  K=[]
  for i in range(n):
    K.append(list(input()))
  f=sys.stdin.readline()
  A.append(test(K))
mini=100000
a=min(A[0]+A[1]+2*n*n-A[2]-A[3],A[0]+A[2]+2*n*n-A[1]-A[3],A[0]+A[3]+2*n*n-A[2]-A[1])
b=min(A[1]+A[2]+2*n*n-A[0]-A[3],A[1]+A[3]+2*n*n-A[2]-A[0])
c=A[2]+A[3]+2*n*n-A[1]-A[0]
mini=min(a,b,c)
print(mini)
