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...
# 8クイーン問題
from itertools import permutations
k = int(input())
S = set(tuple(map(int, input().split())) for _ in [0]*k)
A = set()

dirs = [(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)]
QUEEN = 2

for r, c in S:
    A.add((r, c))
    for dy, dx in dirs:
        y, x = r, c
        while 0 <= x+dx < 8 and 0 <= y+dy < 8:
            y += dy
            x += dx
            A.add((y, x))

for I in permutations(range(8)):
    T = set(s for s in S)

    for r, c in enumerate(I):
        if (r, c) in S:
            continue
        elif (r, c) in T or (r, c) in A:
            break

        for dy, dx in dirs:
            y, x = r, c
            while 0 <= x+dx < 8 and 0 <= y+dy < 8:
                y += dy
                x += dx
                if (y, x) in T:
                    break
            else:
                continue
            break
        else:
            T.add((r, c))
            continue
        break
    else:
        S = T
        break


for y in range(8):
    for x in range(8):
        if (y, x) in S:
            print('Q', end='')
        else:
            print('.', end='')
    print()

