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 itertools

k = int(input())
X = sorted([list(map(int, input().split())) for _ in range(k)])
for l in list(itertools.permutations(range(8))):
  flag = True
  for x in X:
    if l[x[0]] != x[1]:
      flag = False
  if flag:
    flag2= True
    check = []
    for i in range(8):
      for j in range(1,8-i):
        check.append([i+j,l[i]+j])
        check.append([i+j,l[i]-j])
    for c in check:
      if c[1] < 0 or c[1] > 8:
        continue
      else:
        if c in [[i,l[i]] for i in range(8)]:
          flag2 = False
    if flag2:
      #print(l)
      #print(X)
      #print(check)
      for i in range(8):
        tmp = ['.','.','.','.','.','.','.','.']
        tmp[l[i]] = 'Q'
        print(''.join(tmp))
      break
      
