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)]

indexes = set(range(8))
xs = indexes - {x for _, x in points}
ys = list(indexes - {y for y, _ in points})

result = None
for x_indexes in permutations(xs):
    selected = set(points)
    for i, x in enumerate(x_indexes):
        y = ys[i]
        for sy, sx in selected:
            if abs(sx - x) == abs(sy - y):
                break
        else:
            selected.add((y, x))
            continue
        break
    else:
        result = selected
        break

rows = []
for _ in range(8):
    row = ['.'] * 8
    rows.append(row)

for y, x in result:
    rows[y][x] = 'Q'

for row in rows:
    print(''.join(row))

