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 "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr long double EPS = 1e-8;

long long int N, M, K, L, R, H, W;
//int N, M, K, L, R, H, W;


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

	cin >> N;
	vector<pair<int, int>>v;
	for (int i = 2; i <= N; i += 2) {
		v.push_back({ i,1 });
	}
	for (int i = 2; i <= N; i += 3) {
		for (int j = 2 + ((i + 1) & 1); j <= N; j += 2) {
			v.push_back({ i,j });
		}
	}
	if (N % 3 == 1) {
		for (int j = 2 + ((N + 1) & 1); j <= N; j += 2) {
			v.push_back({ N,j });
		}
	}
	cout << v.size() << endl;
	for (auto i : v) {
		cout << i.first-1 << " " << i.second-1 << endl;
	}
}