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 = input()
pieces = []
for i in range(4):
  board = []
  for j in range(n):
    board.append([int(x) for x in raw_input()])
  pieces.append(board)
  if i != 3:
    a = raw_input()

min_squares = (n*2)**2
for i in range(4):
  for j in range(4):
    if i == j:
      continue
    for k in range(4):
      if i == k or j == k:
        continue
      newboard = [pieces[i],pieces[j],pieces[k],pieces[6-i-j-k]]
      chessboard = []
      for a in range(n):
        chessboard.append(newboard[0][a]+newboard[1][a])
      for a in range(n):
        chessboard.append(newboard[2][a]+newboard[3][a])
      switch = 0
      for row in range(n*2):
        for column in range(n*2):
          if (row+column)%2 == 1 and chessboard[row][column] == 0:
            switch += 1
          elif (row+column)%2 == 0 and chessboard[row][column] == 1:
            switch += 1
      if switch < min_squares:
        min_squares = switch
      switch = 0
      for row in range(n*2):
        for column in range(n*2):
          if (row+column)%2 == 1 and chessboard[row][column] == 1:
            switch += 1
          elif (row+column)%2 == 0 and chessboard[row][column] == 0:
            switch += 1
      if switch < min_squares:
        min_squares = switch       
        
print min_squares
      
  