Connected Checkerboard

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

inputFormat

Input

The input is given from Standard Input in the following format:

N

outputFormat

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

样例

2

1
1 0

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