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

row = list(range(0,8))
for i in q:
    row.remove(i[0])
col = list(range(0,8))
for i in q:
    col.remove(i[1])

for i in itertools.permutations(list(range(0,8-k)),8-k):
    queens = []
    for j in range(k):
        queens.append(q[j])
    for j in range(8-k):
        queens.append([row[j],col[i[j]]])
    flg = True
    for j in itertools.combinations(queens,2):
        if abs((j[0][0]-j[1][0])/(j[0][1]-j[1][1])) == 1:
            flg = False
    if flg == True:
        break

# print(queens)
lit = [[]  for _ in range(8)]
for i in range(8):
    for j in range(8):
        lit[i].append('.')
for i in queens:
    lit[i[0]][i[1]] = 'Q'

for i in range(8): print(''.join(map(str,lit[i])))
