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, product
from copy import deepcopy
k = int(input())
rc = [tuple(map(int, input().split())) for _ in range(k)]

for i in permutations(range(8), 8):#product(rx, ry):
    se = set(rc)
    bitmap = [0]*8
    #for i in bitmap: print(f'{i:08b}')
    for y,x in enumerate(i):
        bitmap[y] = 128>>x

    flag = False
    for i in se:
        if not (bitmap[i[0]] & 128>>i[1]):
            flag = True
            break
    if flag:
        continue
    left,down,right = 0,0,0
    for i in bitmap:
        if (left | down | right) & i:
            break
        left = (left | i)<<1
        down = down | i
        right = (right | i)>>1
    else:
        for i in bitmap:
            print('{:08b}'.format(i).replace('0','.').replace('1','Q'))

