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())
RC = [list(map(int,input().split())) for _ in range(K)]
P = list(itertools.permutations([0,1,2,3,4,5,6,7]))
PP = []
for p in P:
    for rc in RC:
        if p[rc[0]] != rc[1]:
            break
    else:
        PP.append(p)
for pp in PP:
    for i in range(8):
        for j in range(1,8):
            if i+j <= 7 and (pp[i]+j == pp[i+j] or pp[i]-j == pp[i+j]):
                break
            if i-j >= 0 and (pp[i]+j == pp[i-j] or pp[i]-j == pp[i-j]):
                break
        else:
            continue
        break
    else:
        ppp = pp
        break
for p in ppp:
    print('.......'[:p] + 'Q' + '.......'[p:])
