#include <iostream>

using namespace std;

#define N 8
#define FREE -1
#define NOT_FREE 1

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

bool X[N][N];

void initialize(){
	for(int i=0;i<N;i++) {
		row[N]=FREE;
		col[N]=FREE;
	}
	for(int i=0;i<2*N-1;i++){
		dpos[i]=FREE;
		dneg[i]=FREE;
	}
}

void printBoard(){
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			if(X[i][j]){
				if(row[i]!=j) return;
			}
		}
	}
	
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			cout << ((row[i]==j)?"Q":".");
		}
		cout<<endl;
	}
}

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

int main() {
	
	initialize();
	
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			X[i][j] = false;
		}
	}
	
	int k;cin>>k;
	
	for(int i=0;i<k;i++){
		int r,c;cin>>r>>c;
		X[r][c]=true;
	}
	
	recursive(0);
	
	
	return 0;
}
### Prompt

Your challenge is to write a cpp solution to the following 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.

<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...

### Response

```cpp
#include <iostream>

using namespace std;

#define N 8
#define FREE -1
#define NOT_FREE 1

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

bool X[N][N];

void initialize(){
	for(int i=0;i<N;i++) {
		row[N]=FREE;
		col[N]=FREE;
	}
	for(int i=0;i<2*N-1;i++){
		dpos[i]=FREE;
		dneg[i]=FREE;
	}
}

void printBoard(){
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			if(X[i][j]){
				if(row[i]!=j) return;
			}
		}
	}
	
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			cout << ((row[i]==j)?"Q":".");
		}
		cout<<endl;
	}
}

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

int main() {
	
	initialize();
	
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			X[i][j] = false;
		}
	}
	
	int k;cin>>k;
	
	for(int i=0;i<k;i++){
		int r,c;cin>>r>>c;
		X[r][c]=true;
	}
	
	recursive(0);
	
	
	return 0;
}
```