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 try_set(v):
    def print_board():
        for (r, c) in preset:
            if queen_pos[r] != c:
                return
        for pos in queen_pos:
            for c in range(8):
                print('Q' if c == pos else '.', end='')
            print()

    for h in range(8):
        if all((horizontal[h], dip_positive[v+h], dip_negative[v-h+7])):
            queen_pos[v] = h
            if v == 7:
                print_board()
            else:
                horizontal[h] = dip_positive[v+h] = dip_negative[v-h+7] = False
                try_set(v + 1)
                horizontal[h] = dip_positive[v+h] = dip_negative[v-h+7] = True

n = int(input())
queen_pos = [None] * 8
preset = [[pre for pre in map(int, input().split())] for _ in range(n)]
horizontal = [True] * 8
dip_positive = [True] * 15
dip_negative = [True] * 15
try_set(0)