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.

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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...
num_queen = 8

def check_puttable(candidate, queens):
    cx, cy = candidate
    for queen in queens:
        qx, qy = queen
        if cx == qx or cy == qy or abs(cx - qx) == abs(cy - qy):
            return False
    return True

def create_candidates(queens):
    return [(i, j) for i in range(num_queen) for j in range(num_queen)
            if check_puttable((i,j), queens)]

def add_queen(queens):
    if len(queens) == num_queen: return queens
    candidates = create_candidates(queens)
    for candidate in candidates:
        _queens = add_queen(queens | {candidate})
        if _queens: return _queens

def show_queens(queens):
    for i in range(num_queen):
        for j in range(num_queen):
            if (i, j) in queens:
                print("Q", end="")
            else:
                print(".", end="")
        print("")

N = int(input())
queens = set()
for _ in range(N):
    i, j = map(int, input().split())
    queens.add((i, j))

queens = add_queen(queens)
show_queens(queens)

