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 permutations

n = int(input())
li = [list(map(int,input().split())) for _ in range(n)]
chess = [["." for i in range(8)]for j in range(8)]

for i in range(8):
    chess[i][i] = "Q"

point = 0

# 行のchessの並べ方を探索
for patern in permutations(chess):
    for y,x in li:
        if patern[y][x] != "Q":
            break
    else:
        # 斜めにもQが一つしかないかを判定
        ld = [0]*15 # i+jの合計を記録（左下斜め方向）
        rd = [0]*15 # 7-i+jの合計を記録（右下斜め方向）
        for i in range(8):
            for j in range(8):
                if patern[i][j] == "Q":
                    ld[i+j] += 1
                    rd[i+(7-j)] += 1
        for k in range(15):
            # 斜め方向には１つしかQがあってはならない
            if rd[k] > 1 or ld[k] > 1:
                break
        else:
            for l in patern:
                print("".join(l))
