#!/usr/bin/env python
# coding=utf-8

"""615. The millionth number with at least one million prime factors
https://projecteuler.net/problem=615

Consider the natural numbers having at least 5 prime factors, which don't have
to be distinct.  
Sorting these numbers by size gives a list which starts with:

  * 32=2⋅2⋅2⋅2⋅2
  * 48=2⋅2⋅2⋅2⋅3
  * 64=2⋅2⋅2⋅2⋅2⋅2
  * 72=2⋅2⋅2⋅3⋅3
  * 80=2⋅2⋅2⋅2⋅5
  * 96=2⋅2⋅2⋅2⋅2⋅3
  * ...

So, for example, the fifth number with at least 5 prime factors is 80.

Find the millionth number with at least one million prime factors.  
Give your answer modulo 123454321.
"""
