Score : $800$ points

Problem Statement

There are some number of bowling pins on a plane. Four people are observing the pins from different angles. Is it possible that one of the observers sees much more pins than the others?

Let's model the pins as a set of points on an $xy$-plane. The image below shows the positions of the four observers. Formally,

• For observer A, two pins overlap if their $y$-coordinates are the same.
• For observer B, two pins overlap if their values of ($x$-coordinate minus $y$-coordinate) are the same.
• For observer C, two pins overlap if their $x$-coordinates are the same.
• For observer D, two pins overlap if their values of ($x$-coordinate plus $y$-coordinate) are the same.

Let $a, b, c, d$ be the number of pins the observers A, B, C, D see, respectively.

Construct any arrangement of bowling pins that satisfies the following constraints:

• $d \geq 10 \cdot \max \{ a, b, c \}$
• The number of pins is between $1$ and $10^5$, inclusive.
• The coordinates are integers between $0$ and $10^9$, inclusive.
• No two pins are placed at exactly the same place.

Input

There is no input.

Output

Print the answer in the following format, where $N$ is the number of pins and $(x_i, y_i)$ are the coordinates of the $i$-th pin:

$N$

$x_1$ $y_1$

$:$

$x_N$ $y_N$

It must satisfy the conditions in the statement.

9
1 1
1 5
2 7
4 4
5 3
6 8
7 5
8 2
8 7

This sample output is provided for the sake of showing the output format and is not correct.

It matches the picture in the statement.

Here, $d = 8$ and $a = b = c = 7$. Nice try, but not enough to get AC.