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...
k=int(input())
l=[]


for _ in range(k):
  l.append(list(map(int, input().split())))
import itertools
for s in itertools.permutations(range(8)):
  t=[]
  for _ in range(8):
    t.append(([s[_], _]))
  for z in l:
    if not (z in t):
      break
  else:
    #print(t)
    for a in range(7):
      for b in range(a+1, 8): # 2つの点を探してのループ
        if abs(t[a][0]-t[b][0])==abs(t[a][1]-t[b][1]):
          break
      else:
        continue
      break
    else:
      tt=sorted(t)
      #print(sorted(t))
      for _ in range(8):
        if tt[_][1]==0:
          print("Q.......")
        else:
          print("."*tt[_][1]+"Q"+"."*(7-tt[_][1]))
    continue
    
  


