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...
#include <stdio.h>

#define N 8
#define free -1
#define notfree 1

int row[N], col[N], dpos[2*N -1],dneg[2*N-1];

int X[N][N];

void printBoard() {
  int i,j;
  for(i=0;i<N;i++){
    for(j=0;j<N;j++){
      if(X[i][j]){
        if(row[i] != j)return;
      }
    }
  }
  for(i = 0;i<N;i++){
    for(j = 0;j<N;j++){
      if(row[i] == j)printf("Q");
      else printf(".");
    }
    printf("\n");
  }
}

void recursive(int i){
  int j;
  if(i == N){
    printBoard();
    return;
  }
  for(j=0;j<N;j++){
    if(notfree == col[j] || notfree == dpos[i + j] || notfree ==dneg[i-j+N-1])continue;
    row[i] = j;
    col[j] = dpos[i + j] = dneg[i-j+N-1]= notfree;
    recursive(i+1);
    row[i] = col[j] = dpos[i + j] = dneg[i - j + N -1] = free;
  }
}

int main(){
  int i;
  for(i = 0;i<N;i++){
    row[i] = free;
    col[i] = free;
  }
  for(i = 0;i<2*N-1;i++){
    dpos[i] = free;
    dneg[i] = free;
  }
  int j;
  for(i=0;i<N;i++){
    for(j=0;j<N;j++){
      X[i][j] = 0;
    }
  }
  int k;
  scanf("%d",&k);
  int r,c;
  for(i = 0;i<k;i++){
    scanf("%d %d",&r,&c);
    X[r][c] = 1;
  }
  recursive(0);
  return 0;
}