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...
import itertools
K=int(input())
R=[]
C=[]
RCd={}
rflag=[ 0 for _ in range(8) ]
for i in range(K):
  r,c=map(int,input().split())
  R.append(r)
  C.append(c)
  RCd[r]=c
  rflag[r]=1

l=[ i for i in range(8) ]
P=itertools.permutations(l,8)
for p in P:
  p=list(p)
  flag=0
  for i in range(8):
    if rflag[i]==1 and p[i]!=RCd[i]:
      flag=1
      break
    for j in range(8):
      if i==j: continue
      if abs(i-j)==p[i]-p[j]:
        flag=1
        break
  #cleared
  if flag==1:continue
  for i in range(8):
    ans='........'
    print(ans[:p[i]]+'Q'+ans[p[i]+1:])
  exit()
