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 sys
import itertools
import copy
input = sys.stdin.readline

n = int(input())
q = [tuple(map(int,input().split())) for _ in range(n)]

px = [0,1,2,3,4,5,6,7]
py = [0,1,2,3,4,5,6,7]
for i in q:
    px.remove(i[0])
    py.remove(i[1])

for v in itertools.permutations(py):
    r_q = copy.deepcopy(q)
    for x,y in zip(px,v):
        for c_q in r_q:
            if c_q[0] == x or c_q[1] == y or abs(c_q[0] - x) == abs(c_q[1]-y):
                break
        else:
            r_q.append((x, y))
            continue
        break
    else:
        board = [['.' for _ in range(8)] for _ in range(8)]
        for i in range(8):
            board[r_q[i][0]][r_q[i][1]] = "Q"
        for i in range(8):
            for j in range(8):
                print (board[i][j],end='')
            print ('')
        exit (0)



