立方体 - المسألة

#15568. 立方体

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AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

编写一个程序，读入一个自然数 $N$，并将其分解为最少数量的完全立方数之和。程序应当找到 $m_1, m_2, \dots, m_k$，使得每个 $m_i$ 均为自然数，$m_1^3 + m_2^3 + \dots + m_k^3 = N$，且 $k$ 最小。

输入格式

输入仅包含一行，为一个自然数 $N$ ($1 \le N \le 44,777,444$)。

输出格式

你的程序应当输出恰好两行。

第一行包含数字 $k$ —— 最少的完全立方数个数。

第二行包含 $k$ 个由空格分隔的自然数，它们的立方和为 $N$。

样例

输入样例 1

输出样例 1

7
2 2 2 2 2 1 1

输入样例 2

输出样例 2

3
3 2 2

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