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.