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 random

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


def solve():
    global qs
    if len(qs) == 8:
        return True

    # モンテカルロ的に探索
    ry, rx = random.randint(0, 7), random.randint(0, 7)
    for y in range(8):
        y = (y+ry) % 8
        for x in range(8):
            x = (x+rx) % 8
            f = False
            for qy, qx in qs:
                dy, dx = abs(y-qy), abs(x-qx)
                if qy == y or qx == x or dy == dx:
                    f = True
                    break
            if not f:
                qs.append([y, x])
                if solve():
                    return
                qs.pop(-1)
    return False


solve()

for y in range(8):
    v = ""
    for x in range(8):
        if [y, x] in qs:
            v += "Q"
        else:
            v += "."
    print(v)

