task

Bounded tuples

There are $$$n$$$ points on the line, the position of $$$i$$$ th point is $$$p[i]$$$. there are Q querys. you will got a segment which length is $$$D[i]$$$, ask at least how many segments are needed to cover all points.

$$$ 1 \le n \le 10^5 $$$, $$$ 1 \le p[i] \le 10^9 $$$, $$$ 1 \le q \le 10^5 $$$

n points on 2D-plane. $$$n \ge 3$$$.

Exist three points a,b,c that $$$1 \le \frac{dis(a,b)}{dis(a, c)} \le \frac{n+1}{n-1}$$$.

How to prove that?