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...
from itertools import permutations
k=int(input())
A=[list(map(int,input().split())) for _ in range(k)]

for i in permutations(range(8)):
    if len(set([j+k for j,k in enumerate(i)]))!=8:continue
    if len(set([j-k for j,k in enumerate(i)]))!=8:continue
    flag=1
    for x,y in A:
        if i[x]!=y:flag=0
    if flag:
        for num in i:
            point=["."]*8
            point[num]="Q"
            print("".join(point))
