Favourite Number

Time limit1sMemory limit512 MB

Summary

Given K, list every positive integer A such that both A and A+K have an odd number of divisors.

Level: Medium5 of 10
Topics: Math, Number theory, Implementation, Brute force
Solved: No attempts yet

Problem

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.

Input

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

Output

On the first line, print the number of possible values of A. On the second line, print all possible values of A in ascending order, separated by a single space.

Hint

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

Examples2

Example 1
Input
```
1
```
Expected output
```
0
```
Example 2
Input
```
2
```
Expected output
```
1
-1
```