Peaceful Sets#5441
A group of mathematicians is organizing battles between natural numbers. The outcome of a battle between two natural numbers is generally random, but it adheres to this rule: if one number is at least twice as large as the other, the larger number always wins; otherwise, either number can win.
A battle is termed uninteresting if its outcome is predetermined. A set of natural numbers is considered peaceful if every battle between any pair of different numbers within this set is uninteresting. The strength of a set is defined as the sum of its numbers. How many peaceful sets of natural numbers with a strength of exist?
A single integer (1 \le n \le 2000).
Output a single integer representing the number of peaceful sets of natural numbers with a strength of .
Example 1
Example 2