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
K = int(input())
Q = [[int(i) for i in input().split()] for _ in range(K)]
li = list(range(8))
P = itertools.permutations(li, 8)

for p in P:
    is_ok = True
    for row, col in Q:
        if(p[row]!=col):
            is_ok = False
            break
    else:
        for ind,i in enumerate(p):
            for x in range(8):
                if(ind==x):
                    continue
                if(p[x]==i+x-ind or p[x]==i-(x-ind)):
                    is_ok = False
    if(is_ok):
        break
ans = [['.']*8 for _ in range(8)]
for ind, i in enumerate(p):
    ans[ind][i] = 'Q'
    print(*ans[ind], sep='')
     
