Problem: We have an N×N checkerboard.

From the square at the upper left corner, a square that is i squares to the right and j squares below is denoted as (i, j). Particularly, the square at the upper left corner is denoted as (0, 0).

Each square (i, j) such that i+j is even, is colored black, and the other squares are colored white.

We will satisfy the following condition by painting some of the white squares:

* Any black square can be reached from square (0, 0) by repeatedly moving to a black square that shares a side with the current square.



Achieve the objective by painting at most 170000 squares black.

Constraints

* 1 \leq N \leq 1,000

Input

The input is given from Standard Input in the following format:


N


Output

Print the squares to paint in the following format:


K
x_1 y_1
x_2 y_2
:
x_K y_K


This means that a total of K squares are painted black, the i-th of which is (x_i, y_i).

Judging

The output is considered correct only if all of the following conditions are satisfied:

* 0 \leq K \leq 170000
* 0 \leq x_i, y_i \leq N-1
* For each i, x_i + y_i is odd.
* If i \neq j, then (x_i, y_i) \neq (x_j, y_j).
* The condition in the statement is satisfied by painting all specified squares.

Examples

Input

2


Output

1
1 0


Input

4


Output

3
0 1
2 1
2 3

Solution (in CPP):

Solution:
#include"bits/stdc++.h"
using namespace std;

int n;

#define MAX 1002
int room[MAX][MAX];

int main(){
	cin>>n;
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			room[i][j]=0;
			if((i+j)&1)continue;
			room[i][j]=true;
		}
	}
	for(int i=0;i<n;i++){
		room[i][0]=true;
	}
	for(int i=0;i<n;i++){
		if(i==n-1||i%3==0){
			
		}
		else{
			continue;
		}
		for(int j=0;j<n;j++){
			room[i][j]=true;
		}
	}
	/*for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			cout<<room[i][j];
		}
		cout<<endl;
	}*/
	vector<pair<int,int> > v;
	for(int i=0;i<n;i++){
		for(int j=0;j<n;j++){
			if((i+j)%2==0)continue;
			if(room[i][j]){
				v.push_back(make_pair(i,j));
			}
		}
	}
	cout<<v.size()<<endl;
	for(auto el:v){
		cout<<el.first<<" "<<el.second<<endl;
	}
	return 0;
}