Points, Lines, Triangles and Graphs

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You are given an integer $k$. You want to choose $n$ points on the plane and join some pairs of those points with line segments (let us call them edges), such that :  $n \lt 510$  Any two points are distinct  No three points are collinear  The points have nonnegative integer coordinates $\leq 10^9$.  No two edges (drawn line segments) intersect at a point which is not an endpoint of either edge.  The number of triangles in the figure is exactly $k$. Note : A triangle means a triple of points such that there is an edge between any two of them. It is guaranteed that it is possible to select a set of points and line segments satisfying the above conditions. ###Input:  The only line of the input contains $k$, the number of required triangles. ###Output:  In first line print two integers, $n$ and $m$, the number of chosen points and number of line segments (edges) drawn between them. They must satisfy $1 \leq n \lt 510$ and $0 \leq m \leq \frac{n(n1)}{2}$  $i^{\text{th}}$ of the next $n$ lines should contain two space separated integers, $x_i, y_i$ denoting the $i^{th}$ chosen point. The coordinates must be nonnegative and $\leq 10^9$, i.e. $0 \leq x_i, y_i \le 10^9$.  $i^{\text{th}}$ of the next $m$ lines should contain two integers $u_i$ and $v_i$, denoting a line segment connecting the $u_i^{th}$ chosen point and the $v_i^{th}$ chosen point. $ 1 \leq u_i, v_i \leq n$ should be satisfied. No edge should be printed more than once. If there are multiple solutions, you can print any of them. ###Constraints  $ 1 \leq k \leq 1500$ ###Sample Input: ``` 2 ``` ###Sample Output: ``` 4 5 0 0 0 1 1 0 1 1 1 2 1 3 2 3 2 4 3 4 ``` ###Explanation: The figure shows the configuration corresponding to the given output. It contains 4 points, and 5 edges. Clearly there are 2 triangles, as the input requires it to be. ![After second second](https://codechef_shared.s3.amazonaws.com/download/Images/TST18KGP/POLITR... =275x275)Author:  jtnydv25 
Editorial  https://discuss.codechef.com/problems/POLITRI 
Tags  jtnydv25 
Date Added:  12122018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
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