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())

points = {tuple(map(int, input().split())) for _ in range(k)}

for perm in permutations(range(8), 8):
    test = {(i, perm[i]) for i in range(8)}
    if test & points == points:
        flg = 0
        for x, y in test:
            diag = {(x - i, y - i) for i in range(1, min(x, y) + 1)} | {(x + i, y + i) for i in range(1, min(7 - x, 7 - y) + 1)} | {(x - i, y + i) for i in range(1, min(x, 7 - y) + 1)} | {(x - i, y + i) for i in range(1, min(7 - x, y) + 1)}
            if diag & test == set():
                flg += 1
        if flg == 8:
            ans = test
            break

for i in range(8):
    col = ""
    for j in range(8):
        if (i,j) in ans:
            col += "Q"
        else:
            col += "."
    print(col)

