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 = []
for i in range(k):
    r,c = map(int, input().split( ))
    Q.append([r,c])
Q.sort()
#print(Q)
for p in itertools.permutations(range(8)):
    flag = True
    Qall = [[i,p[i]] for i in range(8)]
    for q in Q:
        if q[1] != p[q[0]]:
            flag = False
            break
    for j in range(8):
        for l in range(j+1,8):
            if abs(j-l) == abs(p[j]-p[l]):
                flag = False
                break
    if flag:
        break
#print(flag,Qall)    
for i in range(8):
    for j in range(8):
        if [i,j] not in Qall:
            print(".", end = "")
        else:
            print("Q",end="")
    print()
        
                
    


