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...
from itertools import groupby, accumulate, product, permutations, combinations
from copy import copy, deepcopy
def solve():
    k = int(input())
    minus = []
    plus = []
    dic = {}
    for i in range(k):
        r,c = map(int, input().split())
        dic[r] = c
        minus.append(r-c)
        plus.append(r+c)
    for p in permutations(range(8),8):
        mi = copy(minus)
        pl = copy(plus)
        for i in range(8):
            if i in dic:
                if dic[i]!=p[i]:
                    break
                else:
                    continue
            mi.append(i-p[i])
            pl.append(i+p[i])
        else:
            if len(set(mi))==8 and len(set(pl))==8:
                break
    ans = []
    for i in p:
        row = ['.']*8
        row[i] = 'Q'
        ans.append(''.join(row))
    return ans
print(*solve(),sep='\n')
