The goal of 8 Queens Problem is to put eight queens on a chess-board such that none of them threatens any of others. A queen threatens the squares in the same row, in the same column, or on the same diagonals as shown in the following figure.

<image>


For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.

Constraints

* There is exactly one solution

Input

In the first line, an integer $k$ is given. In the following $k$ lines, each square where a queen is already placed is given by two integers $r$ and $c$. $r$ and $c$ respectively denotes the row number and the column number. The row/column numbers start with 0.

Output

Print a $8 \times 8$ chess board by strings where a square with a queen is represented by 'Q' and an empty square is represented by '.'.

Example

Input

2
2 2
5 3


Output

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...
board = [["." for i in range(8)] for i in range(8)]
N = int(input())
row = [1] * 8
col = [1] * 8
dpos = [1] * 15
dneg = [1] * 15


for i in range(N):
  x, y = map(int, input().split())
  row[x] = col[y] = dpos[x+y] =dneg[x-y+7] = 0
  board[x][y] = "Q"

def solve(i):
  while i < 8 and not row[i]:
    i += 1
  if i == 8:
    for i in range(8):
      print(''.join(board[i]))
  for j in range(8):
    if not col[j] or not dpos[i+j] or not dneg[i-j+7]:
      continue
    row[i] = col[j] = dpos[i+j] = dneg[i-j+7] = 0
    board[i][j] ='Q'
    solve(i+1)
    row[i] = col[j] = dpos[i+j] =dneg[i-j+7] = 1
    board[i][j] = '.'

solve(0)
