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...
def put_queen(board, pr, pc):
    def check_square(r, c):
        tmp = (pr == r) + (pc == c)
        if tmp:
            return tmp
        return 1 if abs(pr - r) == abs(pc - c) else board[r][c]

    return list(list(check_square(r, c) for c in range(8)) for r in range(8))


def check_board(board):
    return sum(sum(row) for row in board) == 72


def draw_board(board):
    print('\n'.join(''.join('Q' if c == 2 else '.' for c in row) for row in board))


def search_place(board):
    for r, row in enumerate(board):
        for c, square in enumerate(row):
            if square == 0:
                if search_place(put_queen(board, r, c)):
                    return True
    if check_board(board):
        draw_board(board)
        return True
    else:
        return False


n = int(input())
board = list(list(0 for c in range(8)) for r in range(8))

for _ in range(n):
    r, c = map(int, input().split())
    board = put_queen(board, r, c)

search_place(board)