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

n = int(input())
x = [[0]*2 for _ in range(n)]
for i in range(n):
    x[i][0],x[i][1] = map(int,input().split())
y = []
    
a = [i for i in range(8)]
r = list(itertools.permutations(a,len(a)))

for i in r:
    fl = 1
    for j in range(n):
        if i[x[j][0]] != x[j][1]: 
            fl = 0
    if fl == 1:
        an = 1
        for j in range(8):
            for k in range(8):
                if j == k:
                    continue
                else:
                    if i[j]+j == i[k]+k:
                        an = 0
                    if k-j == i[k] - i[j]:
                        an = 0
        if an == 1:
            y = list(i)
            break
            
ans = [['.']*8 for i in range(8)]
for i in range(8):
    ans[i][y[i]] = 'Q'
    print(''.join(ans[i]))
