Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

2

Sample Output 1

1
1 0

Sample Input 2

4

Sample Output 2

3
0 1
2 1
2 3

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

//set many funcs template
//Ver.20190820
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#include<assert.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
void swap(int *a,int *b){int c;c=(*a);(*a)=(*b);(*b)=c;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
void llswap(long long *a,long long *b){long long c;c=(*a);(*a)=(*b);(*b)=c;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
void dbswap(double *a,double *b){double c;c=(*a);(*a)=(*b);(*b)=c;}
void chswap(char *a,char *b){char c;c=(*a);(*a)=(*b);(*b)=c;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(int arr[],int n){
  int i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%d",arr[i]);
  }
  printf("\n");
  return;
}

void getperm(int a[],int n){
  int i,p;
  for(i=0;i<n;i++){
    a[i]=i;
  }
  for(i=n-1;i>=1;i--){
    p=rand()%(i+1);
    swap(&a[p],&a[i]);
  }
}

typedef struct{
    int par;
    int dep;
    int size;
}node;

node uft[1048576];

void resuf(){
    int i;
    for(i=0;i<1048576;i++){
        uft[i].par=i;uft[i].dep=0;uft[i].size=1;
    }
    return;
}

int find(int x){
    if(uft[x].par==x){return x;}
    else{uft[x].par=find(uft[x].par);return uft[x].par;}
}

void uni(int x,int y){
    int xp,yp;
    xp=find(x);yp=find(y);
    if(xp==yp){return;}
    if(uft[xp].dep>uft[yp].dep){
        uft[yp].par=xp;
        uft[xp].size+=uft[yp].size;
    }
    else{
        uft[xp].par=yp;
        uft[yp].size+=uft[xp].size;
        if(uft[xp].dep==uft[yp].dep){uft[yp].dep++;}
    }
    return;
}

int size(int x){
    x=find(x);
    return uft[x].size;
}

int n;
int rx[262144],ry[262144],rc=0;

void checkadd(int x,int y){
  if(x<0 || n<=x){return 0;}
  if(y<0 || n<=y){return 0;}
  int i,v=-1,r=0,p,q;
  for(i=0;i<4;i++){
    p=x+dx4[i];
    q=y+dy4[i];
    if(p<0 || n<=p){continue;}
    if(q<0 || n<=q){continue;}
    if(v==-1){v=find(p*1024+q);}
    else if(v!=find(p*1024+q)){r=1;break;}
  }
  if(r==1){
    rx[rc]=x;ry[rc]=y;
    rc++;
    for(i=0;i<4;i++){
      p=x+dx4[i];
      q=y+dy4[i];
      if(p<0 || n<=p){continue;}
      if(q<0 || n<=q){continue;}
      uni(p*1024+q,x*1024+y);
    }
  }
  return;
}

void rep(int x,int y,int k){
  if(k!=1){
    rep(x-k,y,k/2);
    rep(x+k,y,k/2);
    rep(x,y-k,k/2);
    rep(x,y+k,k/2);
  }
  checkadd(x,y);
  return;
}

int main(void){
  resuf();
  int i,j,m,k,a,b,c,h,w,r=0,l,t;
  scanf("%d",&n);
  if(n==1){printf("0\n");return 0;}
  h=((n+1)/2);w=((n-1)/2);
  rep(h,w,512);
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      if((i+j)%2==0){continue;}
      checkadd(i,j);
    }
  }
  printf("%d\n",rc);
  for(i=0;i<rc;i++){
    printf("%d %d\n",rx[i],ry[i]);
  }
  return 0;
}