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
def getDif(l1, l2, n):
  r = 0
  for i in range(len(l1)):
    for j in range(n):
      if l1[i][j] != l2[i][j]: r += 1
  return r
  

n = int(input())
boards, type1, type2, num_t1, num_t2, res = [], [], [], 0, 0, 0
for i in range(4*(n + 1) - 1):
  boards.extend([input()])

boards = list(filter(lambda a: a != "", boards))
boards = [boards[x:x+n] for x in range(0, len(boards), n)]
    
c, r1, r2 = 0, "", ""
for i in range(n):
  if c % 2 == 0: r1 += "1"; r2 += "0"
  else: r1 += "0"; r2 += "1"
  c += 1
    
c = 0
for i in range(n):
  if c % 2 == 0: type1.append(r1); type2.append(r2)
  else: type1.append(r2); type2.append(r1)
  c += 1  

for index, i in enumerate(boards):
  if i == type1 and num_t1 < 2: 
    num_t1 += 1
    boards.pop(index)
  elif i == type2 and num_t2 < 2: 
    num_t2 += 1
    boards.pop(index)   

while num_t2 < 2 or num_t1 < 2:
  if num_t1 < 2:
    dif_min, pos = float("inf"), -1
    for index, i in enumerate(boards):
      dif = getDif(i, type1, n)
      if dif < dif_min: 
        dif_min = dif
        pos = index

    num_t1 += 1
    res += dif_min
    boards.pop(pos)
    
  if num_t2 < 2:
    dif_min, pos = float("inf"), -1
    for index, i in enumerate(boards):
      dif = getDif(i, type2, n)
      if dif < dif_min: 
        dif_min = dif
        pos = index
    
    num_t2 += 1
    res += dif_min
    boards.pop(pos)
  
print(res)