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;
#define ALL(A) (A).begin(),(A).end()
#define ll long long
const ll mod = 1e9+7;
const ll INF = 2*1e18;
const int inf = 1e9+7;

char s[1005][1005];
int main(void){
	int N;
	cin >> N;
	for(int i=0;i<N;i++){
		for(int j=0;j<N;j++){
			if((i+j)%2==0){
				s[i][j] = '#';
			}else{
				s[i][j] = '.';
			}
		}
	}
	int ans = 0;
	for(int i=0;i<N;i++){
		if(s[i][0] =='.'){
			ans ++;
			s[i][0] = 'x';
		}
		if(s[N-1][i] =='.'){
			ans++;
			s[N-1][i] = 'x';
		}
	}
	for(int i=0;i<N;i++)
		if(i%3==0){
			for(int j=0;j<N;j++){
				if(s[i][j] =='.'){
					ans++;
					s[i][j] = 'x';
				}
			}
		}
	
	cout << ans << endl;
	for(int i=0;i<N;i++)for(int j=0;j<N;j++){
		if(s[i][j] =='x')cout << i << " " << j << endl;
	}
}