Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

8 Queens Problem

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.

For a given chess board where $k$ queens are already placed, find the solution of the 8 queens problem.

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 '.'.

Constraints

There is exactly one solution

Sample Input 1

2
2 2
5 3

Sample Output 1

......Q.
Q.......
..Q.....
.......Q
.....Q..
...Q....
.Q......
....Q...

Solution in Ruby (judge verdict: Accepted)

def printQueen(queen)
#  p queen
  8.times{|i|
    str = ""
    8.times{|j|
      if queen[i] == j then
        str << "Q"
      else
        str << "."
      end
    }
    puts str
  }
end

def setQueen(queen)
  idx = queen.index(nil)
  ref = [0,1,2,3,4,5,6,7] - queen
  if idx == nil then
    if check(queen) == 1 then
      printQueen(queen)
      exit
    end
    return
  end
  tmp = queen.clone
  ref.each{|j|
    tmp[idx] = j
    setQueen(tmp)
  }
end

def check(queen)
  8.times{|i|
    (i+1).upto(7){|j|
      return 0 if queen[i] == queen[j] || (queen[i] - queen[j]).abs == j - i
    }
  }
  return 1
end


n = gets.to_i
queen = Array.new(8){nil}

n.times{
  x, y = gets.split.map(&:to_i)
  queen[x] = y
}

setQueen(queen)