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
import collections

k = int(input())

Z = []

for kk in range(k):
    x, y = map(int, input().split())
    Z.append((x, y))

a = ()

for v in itertools.permutations(range(8)):
    X = []
    Y = []
    V = []
    for i, vv in enumerate(v):
        V.append((i, vv))
    flag = False
    for kk in range(k):
        if Z[kk] not in V:
            flag = True
            break
    if flag:
        continue
    for i, vv in enumerate(v):
        X.append(i+vv)
        Y.append(i-vv)
    x = collections.Counter(X)
    y = collections.Counter(Y)
    if x.most_common()[0][1] >= 2 or y.most_common()[0][1] >= 2:
        continue
    a = v
    break

for i in range(8):
    print('.'*a[i] + 'Q' + '.'*(7-a[i]))
