406340: GYM102367 B Favourite Number

Volodymyr's favourite number is $$$A$$$ and it has an odd number of positive divisors. When you add $$$K$$$ to this number, the resulting sum also has an odd number of positive divisors. Given $$$K$$$, find all possible values of $$$A$$$, Volodymyr's favourite number.

The only line of input contains $$$K$$$, a positive integer not exceeding $$$10^9$$$.

On the first line, print the number of possible values of $$$A$$$. If the number of such values is greater than zero, on the second line print all possible values of $$$A$$$ in ascending order, separated by a single space.

1

0

2

1
-1

Note that since zero has infinitely many divisors, it cannot be classified as a number with an odd number of divisors.