C. Even Picturetime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputLeo 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: The picture is connected, that is, it is possible to get from any gray cell to any other by following a chain of gray cells, with each pair of adjacent cells in the path being neighbours (that is, sharing a side). Each gray cell has an even number of gray neighbours. There are exactly n gray cells with all gray neighbours. The number of other gray cells can be arbitrary (but reasonable, so that they can all be listed).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.InputThe 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.OutputIn 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.ExampleInput
4
Output
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
NoteThe answer for the sample is pictured below:  
4

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 
['constructive algorithms', '*1500']