Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

2

Sample Output 1

1
1 0

Sample Input 2

4

Sample Output 2

3
0 1
2 1
2 3

Solution in Ruby (2.3.3) (judge verdict: Accepted)

#!/usr/bin/ruby
N=gets.to_i
r=1.step(N-2,2).flat_map{|i|[[0,i],[i,0]]}
r+=N.times.select{|i|(i+N)%2==0}.flat_map{|i|[[N-1,i],[i,N-1]]}
1.step(N-2,3){|j|
	1.step(N-2){|i|
		r<<[i,j] if (i+j)%2==1
	}
}
p r.size
puts r.map{|e|e*' '}