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())
rc_sub = {}
for _ in range(k):
    r, c = [int(i) for i in input().split()]
    rc_sub[r] = c
board = [["."]*8 for _ in range(8)]

for pp in itertools.permutations(range(8), 8):
    rc = {i: p for (i, p) in enumerate(pp)}
    ok = True
    # 初期配置条件を満たさない場合スキップ
    for k, v in rc_sub.items():
        if rc[k] != v:
            ok = False
            break
    if not ok:
        continue

    # 配置条件（斜め）を満たさない場合スキップ
    for (p1, p2) in itertools.combinations(rc.items(), 2):
        if (p2[0] - p1[0]) / (p2[1] - p1[1]) in (1, -1):
            ok = False
            break

    if ok:
        for k, v in rc.items():
            board[k][v] = "Q"
        break

for line in board:
    print(*line, sep="")
