Sum of Cubes

You are given a natural number $N$. Write $N$ as a sum of cubes of natural numbers using as few terms as possible. That is, find natural numbers $m_1, m_2, \ldots, m_k$ with

$m_1^3 + m_2^3 + \cdots + m_k^3 = N$

where $k$ is as small as possible. The same number may be used more than once.

The first and only line contains the natural number $N$ ($1 \le N \le 44{,}777{,}444$).

Print two lines. The first line contains $k$, the minimum number of cubes. The second line contains $k$ natural numbers whose cubes add up to $N$, separated by single spaces and sorted so that no number is smaller than the number after it.

If several sets of $k$ numbers work, print the one that comes first in lexicographic order. Compare two sets at the first position where they differ, and the set with the smaller number there comes first. For $N = 1729$ both $12^3 + 1^3$ and $10^3 + 9^3$ use two cubes, so the answer is 10 9.