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())
rc = [list(map(int, input().split())) for i in range(k)]

for x in permutations(range(8)):
    flag = False
    for i in rc:
        if x[i[1]] != i[0]:
            flag = True
            break
    if flag:
        continue
    # 斜めの処理
    for i in range(7):
        flag = False
        for j in range(i+1, 8):
            if abs(x[i] - x[j]) == abs(i-j):
                flag = True
                break
        if flag:
            break
    if flag:
        continue
    for i in range(8):
        for j in range(8):
            if i == x[j]:
                print('Q', end='')
            else:
                print('.', end='')
        print()
    break
