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

ii = lambda : int(input())
mi = lambda : map(int,input().split())
li = lambda : list(map(int,input().split()))

n = ii()
A = [tuple(int(i) for i in input().split()) for _ in range(n)]

ban = [['.'] * 8 for i in range(8)]

# for i in A:
#     ban[i[0]][i[1]] = '.'

for i in itertools.permutations(range(8)):
    flg = 0
    for j in A:
        if(i[j[0]] != j[1]):
            flg = 1
            break
    if flg:
        continue

    nc = []
    nc2 = []
    for k,j in enumerate(i):
        nc.append(k + j)
        nc2.append(k-j)
    
    if(len(set(nc)) != 8) |(len(set(nc2)) != 8) :
        continue

    else:
        for k,j in enumerate(i):
            ban[k][j] = 'Q'
        break
    

for i in ban:
    for j in i:
        print(j,end='')
    print('')
    
