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())
q=[list(map(int,input().split())) for _ in range(n)]
l=list(range(8))
Q=list(permutations(l,8))
def OK(s):
    a=list(s)
    b=list(s)
    for i in range(len(s)):
        a[i]-=i
        b[i]+=i
    for i,j in enumerate(a[:-1]):
        if j in a[i+1:]:
            return False
    for i,j in enumerate(b[:-1]):
        if j in b[i+1:]:
            return False
    return True
for i in Q:
    chk=i
    for x,y in q:
        if i[x]!=y:
            chk=[]
            break
    if chk:
        if OK(i):
            A=i
            break
ans=[['.']*8 for _ in range(8)]
for i,j in enumerate(A):
    ans[i][j]='Q'
    print(''.join(map(str,ans[i])))
