Description

At the start, all lights are off (note: off!). The person numbered $1$ comes and turns on all lights whose indices are multiples of $1$. The person numbered $2$ turns off all lights whose indices are multiples of $2$. The person numbered $3$ toggles all lights whose indices are multiples of $3$ (those that are on are turned off, those that are off are turned on), and so on, until the person numbered $N$ finishes.

Given $N$, after $N$ rounds, determine which lights are still on.

Input Format

A single number $N$, representing both the number of lights and the number of rounds.

Output Format

Several numbers, the indices of the lights that are on.

5

1 4

Hint

Constraints

For $100 \%$ of the testdata, $1 \le N \le 2^{40}$.

Additional Notes

Math problem!

Translated by ChatGPT 5