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 sys
import itertools


input = sys.stdin.readline


def cannot_attack(Q):
    for i in range(7):
        sx, sy = Q[i]
        for j in range(i+1, 8):
            tx, ty = Q[j]
            if abs(tx-sx) == abs(ty-sy):
                return False
    return True


def include_fq(sq):
    for e in fq:
        if e not in sq:
            return False
    return True


def main():
    Q = []
    for p in itertools.permutations(range(8)):
        Q = [(i, p[i]) for i in range(8)]
        if cannot_attack(Q) and include_fq(set(Q)):
            break
    for y, x in Q:
        print("."*x+"Q"+"."*(7-x))


if __name__ == "__main__":
    K = int(input())
    fq = [tuple(map(int, input().split())) for _ in range(K)]
    main()
