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())

area = [["."]*8 for i in range(8)]

X = set(range(8))
Y = set(range(8))
A = set()
B = set()

for i in range(k):
    x, y = map(int, input().split())
    area[x][y] = "Q"

    X.remove(x)
    Y.remove(y)
    A.add(x-y)
    B.add(x+y)
for v in itertools.permutations(Y):
    ok = 1
    A_ = A.copy()
    B_ = B.copy()
    for x, y in zip(X, v):
        if x-y in A_ or x+y in B_:
            ok = 0
            break

        A_.add(x-y)
        B_.add(x+y)
    
    if ok:
        for x, y in zip(X, v):
            area[x][y] = "Q"
        break

for i in range(8):
    print("".join(area[i]))

