Sums in threes#2488
Given a natural number , construct a sequence of integers a_{-1}, a_0, a_1, \ldots, a_m such that:
- 0 = a_{-1} = a_0 < a_1 < a_2 < \ldots < a_m \leq n - a_k > \frac{k^3}{56} for all 1 \leq k \leq m - For every x \in \{1, 2, \ldots, n\}, there exist indices i, j, k such that -1 \leq i < j < k \leq m and x = a_i + a_j + a_k
It is guaranteed that such a sequence exists.
The input is a single line containing the integer (n \leq 10^8).
Output the integer on the first line. On the second line, output the sequence of numbers a_1, a_2, \ldots, a_m separated by spaces. If there are multiple solutions, output any of them.
Example 1