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 $n$, $1\le n\le 1000$.

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

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
$T<30$	$0$
$30\le T<50$	$3(T-30)$
$50\le T<100$	$60+\frac{2(T-50)}{5}$
$100\le T<500$	$80+\frac{T-100}{20}$
$T\ge 500$	$100$