|Codeforces Global Round 8|
Leo Jr. draws pictures in his notebook with checkered sheets (that is, each sheet has a regular square grid printed on it). We can assume that the sheets are infinitely large in any direction.
To draw a picture, Leo Jr. colors some of the cells on a sheet gray. He considers the resulting picture beautiful if the following conditions are satisfied:
Leo Jr. is now struggling to draw a beautiful picture with a particular choice of $$$n$$$. Help him, and provide any example of a beautiful picture.
To output cell coordinates in your answer, assume that the sheet is provided with a Cartesian coordinate system such that one of the cells is chosen to be the origin $$$(0, 0)$$$, axes $$$0x$$$ and $$$0y$$$ are orthogonal and parallel to grid lines, and a unit step along any axis in any direction takes you to a neighbouring cell.
The only line contains a single integer $$$n$$$ ($$$1 \leq n \leq 500$$$) — the number of gray cells with all gray neighbours in a beautiful picture.
In the first line, print a single integer $$$k$$$ — the number of gray cells in your picture. For technical reasons, $$$k$$$ should not exceed $$$5 \cdot 10^5$$$.
Each of the following $$$k$$$ lines should contain two integers — coordinates of a gray cell in your picture. All listed cells should be distinct, and the picture should satisdfy all the properties listed above. All coordinates should not exceed $$$10^9$$$ by absolute value.
One can show that there exists an answer satisfying all requirements with a small enough $$$k$$$.
12 1 0 2 0 0 1 1 1 2 1 3 1 0 2 1 2 2 2 3 2 1 3 2 3
The answer for the sample is pictured below: