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 sys
input = lambda: sys.stdin.readline().rstrip() 

def resolve():
    k = int(input())
    rc = [list(map(int, input().split())) for _ in range(k)]
 
    def dfs(d, perm):
        if d==8:
            ok = True
            for i in rc:
                if perm[i[0]]!=i[1]:
                    ok = False
            if ok:
                okok = True
                for j in range(7):
                    for k in range(j+1, 8):
                        if j-perm[j]==k-perm[k] or j+perm[j]==k+perm[k]:
                            okok = False
                if okok:
                    for j in range(8):
                        pos = perm[j]
                        print('.'*pos+'Q'+'.'*(7-pos))
            return perm
        else:
            for i in range(8):
                if i not in perm:
                    dfs(d+1, perm+[i])
    dfs(0, [])

if __name__ == '__main__':
    resolve()
