Determine if chasing points will meet

You are given **N points** in 2D, indexed `0..N-1`, forming a cycle. - At time `t = 0`, point `i` is at coordinates `(xi, yi)`. - All points move **simultaneously** and continuously. - Each point moves with **constant speed** `v = 1`. - At any time `t`, point `i` moves in the direction of the **current position** of point `(i+1) mod N` (i.e., it “chases” the next point). ### Task Write a program that determines whether the points will **all meet at the same location at the same time**. If they do meet, output: 1. The meeting time `T`. 2. The meeting position `(X, Y)`. If they do **not** meet, output `NEVER`. ### Input - Integer `N` (`2 ≤ N ≤ 200`) - `N` lines of real numbers: `xi yi` ### Output - Either `NEVER`, or three real numbers `T X Y`. ### Requirements / Notes - Your numeric outputs should be within `1e-4` absolute error. - You may use numerical simulation (time-stepping) as long as it meets the error requirement and runs efficiently.