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 <iostream>
#include <fstream>
#include <typeinfo>
#include <vector>
#include <stack>
#include <cmath>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cstdio>
#include <queue>
#include <iomanip>
#include <cctype>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<char> vc;
typedef vector<vc> vvc;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-6;
const ll mod=1e9+7;
const vi emp;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,-0};
const int DX[8]={-1,-1,-1,0,0,1,1,1},DY[8]={1,0,-1,1,-1,1,0,-1};

int n;

int main(){
	cin>>n;
	vp a;
	for(int i=0;i<n/3;i++) for(int j=0;j<n;j++) if(i%2==j%2){
		a.push_back(P(j,i*3+1));
	}
	for(int i=0;i<n;i++) if(i%2==1) a.push_back(P(0,i));
	for(int i=0;i<n;i++) if((i+n-1)%2==1) a.push_back(P(i,n-1));
	sort(a.begin(),a.end());
	a.erase(unique(a.begin(),a.end()),a.end());
	int S=a.size();
	cout<<S<<endl;
	for(int i=0;i<S;i++) cout<<a[i].first<<' '<<a[i].second<<endl;
}