Write a program that takes a natural number N and decomposes it as a sum of the minimum number of exact natural cubes. The program should find m₁, m₂, …, m_k, such that each m_i is a natural number, m₁³ +m₂³ +… +m_k³ = N, and k is minimal.

입력 형식

The only line of the input file contains the number N (1 ≤ N ≤ 44,777,444).

출력 형식

Your program should write exactly two lines. The first line contains the number k - the minimum number of natural cubes. The second line contains k space-separated natural numbers - that raised to the power of 3 sum to N.

예제 입력 1

42

예제 출력 1

7
2 2 2 2 2 1 1

예제 입력 2

43

예제 출력 2

3
3 2 2