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

n=int(input())
lst_ini=[list(map(int,input().split())) for _ in range(n)]
row=list(range(8))
col=list(range(8))
for x in lst_ini:
    row.remove(x[0])
    col.remove(x[1])

for x in permutations(col):
    work=lst_ini[:]
    for i in range(8-n):
        work.append([row[i],x[i]])
    
    #対角方向チェック
    for y in work:
        for i in range(8):
            if y[0]==i: continue
            if [i,y[1]-(y[0]-i)] in work : break
            if [i,y[1]+(y[0]-i)] in work : break
        else : continue
        break
    else : break

for i in range(8):
    out=""
    for j in range(8):
        if [i,j] in work : out+="Q"
        else : out+="."
    print(out)

