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 <cstdio>
#include <algorithm>
#include <string>
#include <vector>
#include <map>
#include <set>
using namespace std;

#define mp make_pair

int main() {
        int n;
        scanf("%d", &n);
        set<pair<int, int>> paint;
        for (int y = 0; y < n; y ++) {
                if (y % 6 == 1) {
                        for (int x = 2; x < n; x += 2) {
                                paint.insert(mp(x, y));
                        }
                }
                if (y % 6 == 4) {
                        for (int x = 1; x < n; x += 2) {
                                paint.insert(mp(x, y));
                        }
                }
        }
        for (int y = 0; y < n; y ++) {
                if (y & 1 && !paint.count(mp(0, y))) {
                        paint.insert(mp(0, y));
                }
        }
        for (int x = 0; x < n; x ++) {
                if ((x + n - 1) & 1 && !paint.count(mp(x, n - 1))) {
                        paint.insert(mp(x, n - 1));
                }
        }
        printf("%d\n", (int) paint.size());
        for (auto it : paint) {
                printf("%d %d\n", it.first, it.second);
        }
        return 0;
}