Control C301A P57404

A natural number $n > 0$ is called powerful if, for each prime divisor $p$ of $n$, $p^2$ is also divisor of $n$. For example, $55125 = 3\cdot3\cdot5\cdot5\cdot5\cdot7\cdot7$ is a powerful number, because every prime factor appears, at least, twice.

Your task is to write a program that reads a sequence of numbers $m$ and, for each one, prints all the powerful numbers between 1 and $m$.

Input

The input is a sequence of natural numbers $m > 0$.

Output

For each $m$ of the input, print a line with all the powerful numbers between 1 and $m$, separated by commas and in increasing order.

Observation

Your program must implement and use the function

    bool is_powerful(int n);

that, given an integer strictly positive |n|, indicates if is powerful or is not