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

n = int(input())
q = [list(map(int, input().split())) for _ in range(n)]
for p in permutations(range(8), 8):
    if all(p[i] == j for i, j in q):
        m = [["."] * 8 for _ in range(8)]
        for i, j in enumerate(p):
            m[i][j] = "Q"
        b = True
        for i, j in enumerate(p):
            for k in range(1, 8):
                if 0 <= i + k < 8 and 0 <= j + k < 8:
                    if m[i + k][j + k] == "Q":
                        break
                if 0 <= i - k < 8 and 0 <= j + k < 8:
                    if m[i - k][j + k] == "Q":
                        break
                if 0 <= i + k < 8 and 0 <= j - k < 8:
                    if m[i + k][j - k] == "Q":
                        break
                if 0 <= i - k < 8 and 0 <= j - k < 8:
                    if m[i - k][j - k] == "Q":
                        break
            else:
                continue
            b = False
            break
        if b:
            for a in m:
                print(*a, sep="")
            exit()

