You are walking alone in the woods one night when out of the corner of your eye you see something moving. You turn and see a Large Russian Bear moving towards you.

It turns out this bear is writing a contest problem, and requires a list of Egyptian Fractions (reciprocals of positive integers) whose sum is extremely close to, but not exactly, equal to ~1~.

Input Format

You are given a single integer ~v \in \{-1, 1\}~

Output Format

On the first line, output a single integer ~n~, ~1 \leq n \leq 1000~.

On the second line, output ~n~ integers, ~1 \leq x_i \leq 10^{18}~.

Scoring

If your output is improperly formatted you will receive ~0~ points.

Otherwise, let ~S = \sum_{i = 1}^n \frac{1}{x_i}~. If ~v = 1~ then you must have ~S > 1~ or you will receive ~0~ points. Similarly, if ~v = -1~ then you must have ~S < 1~ or you will recieve ~0~ points.

If you have a valid submission, then you receive points according to the following table, where ~T = -\log_{10}(|1 - S|)~

T	Score
~T < 30~	~0~
~30 \leq T < 50~	~3(T - 30)~
~50 \leq T < 100~	~60 + \frac{2(T - 50)}{5}~
~100 \leq T < 500~	~80 + \frac{T - 100}{20}~
~T \geq 500~	~100~