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 <algorithm>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

#define FOR(i,k,n) for (int (i)=(k); (i)<(n); ++(i))
#define rep(i,n) FOR(i,0,n)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#define all(v) begin(v), end(v)
#define debug(x) cerr<< #x <<": "<<x<<endl
#define debug2(x,y) cerr<< #x <<": "<< x <<", "<< #y <<": "<< y <<endl

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vector<int> > vvi;
typedef vector<ll> vll;
typedef vector<vector<ll> > vvll;
template<class T> using vv=vector<vector< T > >;

int main() {
  int n;
  scanf("%d", &n);
  int m = 170000;
  vi x(m), y(m);
  int k = 0;

  for (int i = 1; i < n; i += 3) {
    for (int j = (i % 2 == 1) ? 0 : 1; j < n; j += 2) {
      x[k] = i;
      y[k] = j;
      k += 1;
    }
  }
  if (n % 3 == 1) {
    for (int i = ((n-1) % 2 == 1) ? 0 : 1; i < n; i += 2) {
      x[k] = n-1;
      y[k] = i;
      k += 1;
    }
  }
  rep (i, n-1) {
    if (i % 2 == 0 || i % 3 == 1) {
      continue;
    }
    x[k] = i;
    y[k] = 0;
    k += 1;
  }
  printf("%d\n", k);
  rep (i, k) {
    printf("%d %d\n", x[i], y[i]);
  }

  return 0;
}