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 int long long   // <-----!!!!!!!!!!!!!!!!!!!

#define rep(i,n) for (int i=0;i<(n);i++)
#define rep2(i,a,b) for (int i=(a);i<(b);i++)
#define rrep(i,n) for (int i=(n)-1;i>=0;i--)
#define rrep2(i,a,b) for (int i=(a)-1;i>=b;i--)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define printV(_v) for(auto _x:_v){cout<<_x<<" ";}cout<<endl
#define printVS(_vs) for(auto _x : _vs){cout << _x << endl;}
#define printVV(_vv) for(auto _v:_vv){for(auto _x:_v){cout<<_x<<" ";}cout<<endl;} cout << endl;
#define printP(_p) cout << _p.first << " " << _p.second << endl
#define printVP(_vp) for(auto _p : _vp) printP(_p);

typedef long long ll;
typedef pair<int, int> Pii;
typedef tuple<int, int, int> TUPLE;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<Pii> vp;
const int inf = 1e9;
const int mod = 1e9 + 7;
typedef vector<vector<int>> Graph;

signed main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);

    int n;
    cin >> n;

    vvi b(n, vi(n));
    rep(i, n) {
        rep(j, n) {
            b[i][j] = (i + j) % 2; // 0:black, 1:white
        }
    }

    int K = 0;
    vvi a = b;
    for (int i = 1; i < n; i += 3) {
        rep(j, n) {
            if (a[i][j]) {
                a[i][j] ^= 1;
                K++;
            }
        }
    }

    rep(j, n) {
        if (a[n-1][j]) {
            a[n-1][j] ^= 1;
            K++;
        }
    }

    rep(i, n) {
        if (a[i][0]) {
            a[i][0] ^= 1;
            K++;
        }
    }

    cout << K << endl;
    rep(i, n) {
        rep(j, n) {
            if (b[i][j] && !a[i][j]) {
                cout << j << " " << i << endl;
            }
        }
    }


}