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 <cstdio>
#pragma warning(disable : 4996)
int n, g[1009][1009];
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < n; j++) {
			if (i == 0 || j == 0 || i == n - 1 || j == n - 1 || (i + j) % 2 == 0) g[i][j] = 1;
			else g[i][j] == 0;
		}
	}
	for (int i = 1; i <= 10; i++) {
		for (int j = 0; j < n; j++) {
			for (int k = 0; k < n; k++) {
				if (((j + k) & ((2 << i) - 1)) == (1 << i) - 1 && !(~k & ((1 << i) - 1))) g[j][k] = 1;
			}
		}
	}
	int c = 0;
	for (int i = 0; i < n; i++) {
		for (int j = (i & 1) ^ 1; j < n; j += 2) {
			c += g[i][j];
		}
	}
	printf("%d\n", c);
	for (int i = 0; i < n; i++) {
		for (int j = (i & 1) ^ 1; j < n; j += 2) {
			if (g[i][j]) printf("%d %d\n", i, j);
		}
	}
	return 0;
}