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 can_put(arr, point):
    for p in arr:
        if p[0] == point[0] or p[1] == point[1] or p[0]-p[1] == point[0]-point[1] or p[0]+p[1] == point[0]+point[1]:
            return False
    return True

K = int(input())
RC = [tuple(map(int,input().split())) for _ in range(K)]
def dfs(arr):
    if len(arr) == 8:
        se = set()
        for a in arr:
            se.add(a)
        for i in range(8):
            for j in range(8):
                if (i,j) in se:
                    print("Q", end="")
                else:
                    print(".", end="")
                if j == 7: print()
        exit()
    for i in range(8):
        for j in range(8):
            if can_put(arr, (i,j)):
                dfs(arr+[(i,j)])
dfs(RC)

