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
def I(): return int(input())
def LI(): return list(map(int,input().split()))
k = I()
rc = [LI() for _ in range(k)]
for a in itertools.permutations(range(8)):
    XY = [[x,y] for x,y in enumerate(a)]
    if len(set([x+y for x,y in XY])) !=8 or len(set([x-y for x,y in XY])) !=8:
        continue
    count = 0
    for r,c in rc:
        if [r,c] in XY:
            count += 1
    if count !=k:
        continue
    board = [['.' for _ in range(8)] for _ in range(8)]
    for x,y in XY:
        board[x][y] = 'Q'
    break
for b in board:
    print(*b,sep='')
