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...
k = int(input())
row = [1] * 8
col = [1] * 8
dpos = [1] * 15
dneg = [1] * 15
X = [['.' for j in range(8)] for i in range(8)]
for i in range(k):
    r, c = map(int, input().split())
    row[r] = col[c] = dpos[r+c] = dneg[r-c+7] = 0
    X[r][c] = 'Q'

def solve(i):
    while i < 8 and not row[i]:i += 1        
    if i == 8:
        for i in range(8):
            print(''.join(X[i]))
    for j in range(8):
        if not col[j] or not dpos[i+j] or not dneg[i-j+7]: continue
        row[i] = col[j] = dpos[i+j] = dneg[i-j+7] = 0
        X[i][j] = 'Q'
        solve(i+1)
        row[i] = col[j] = dpos[i+j] = dneg[i-j+7] = 1
        X[i][j] = '.'
solve(0)
