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())
coords = [tuple(map(int, input().split())) for _ in range(k)]

for item in itertools.permutations(range(8)):
    for x, y in coords:
        if item[x] != y:
            break
    else:
        for i, j in enumerate(item):
            for k in range(1, 8):
                if i+k < 8:
                    if item[i+k] == j+k: break
                    if item[i+k] == j-k: break
                if i-k >= 0:
                    if item[i-k] == j+k: break
                    if item[i-k] == j-k: break
            else:
                continue
            break
        else:
            break

for i in range(8):
    print('.' * item[i] + 'Q' + '.' * (7-item[i]))

