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
p = list(itertools.permutations(range(8)))
n = int(input())
k = [list(map(int,input().split())) for i in range(n)]
for d in p:
    f = True
    for r,c in k:
        if d[r]!=c:
            f = False
    if not f:continue
    for i in range(8):
        for j in range(8):
            if i==j:continue
            if i+d[i]==j+d[j]:
                f = False
            if i-d[i]==j-d[j]:
                f = False
    if f:
        for i in d:
            s = ['.']*8
            s[i]='Q'
            print(''.join(s))
