package main

// Time: O(n^2)
// Space: O(n)
func numTrees(n int) int {
	if n < 3 {
		return n
	}
	trees := map[int]int{
		0: 1,
		1: 1,
		2: 2,
	}
	for c := 3; c <= n; c++ {
		s := 0
		for p := 0; p < c/2; p++ {
			s += trees[p] * trees[c-p-1] * 2
		}
		if (c-1)%2 == 0 {
			p := (c - 1) / 2
			s += trees[p] * trees[p]
		}
		trees[c] = s
	}
	return trees[n]
}