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;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

#define FOR(k,m,n) for(ll (k)=(m);(k)<(n);(k)++)
#define REP(i,n) FOR((i),0,(n))
#define WAITING(str) int str;std::cin>>str;
#define DEBUGING(str) cout<< #str << " " str<<endl

constexpr int INF = (1 << 30);
constexpr ll INFL = (1ll << 60);
constexpr ll MOD = 1000000007;// 10^9+7



int main()
{
	int N;
	set<pair<int, int>> poss;
	cin >> N;

	REP(h, N)REP(w, N) {
		if (h % 3 != 0)continue;
		if ((h + w) % 2 == 1)poss.insert({ h,w });
	}
	REP(h, N)if (h % 2 == 1)poss.insert({ h,0 });
	REP(w, N)if ((N - 1 + w) % 2 == 1)poss.insert({ N - 1,w });

	cout << poss.size() << endl;
	for (auto pos : poss) {
		cout << pos.second << " " << pos.first << endl;
	}

	return 0;
}