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 copy import copy,deepcopy
import itertools
k=int(input())
b=[['.']*8 for i in range(8)]
R=set(range(8))
C=set(range(8))
p=set()
m=set()
for i in range(k):
    r,c=map(int,input().split())
    b[r][c]='Q'
    R.remove(r);C.remove(c)
    p.add(r+c)
    m.add(r-c)
for x in itertools.permutations(C):
    P=p.copy()
    M=m.copy()
    ok=True
    for r,c in zip(R,x):
        if r+c in P:
            ok=0
        P.add(r+c)
        if r-c in M:
            ok=0
        M.add(r-c)
    if(ok):
        for r,c in zip(R,x):
            b[r][c]='Q'
        break
for i in range(8):
    print(''.join(b[i]))
