Find Largest Set of Onion Bags

You are shopping online for some bags of onion. Each listing displays the number of onions that the bag contains. You want to buy a perfect set of onion bags from the entire search results list, onionBags. A perfect set of onion bags, perfect, is defined as: The set contains at least two bags of onion. When the onion bags in the set perfect are sorted in increasing order by count, it satisfies the condition perfect[i] = perfect[i+1] for all 1 ≤ i < n. Here n is the size of the set and perfect[i] is the number of onion in bag i. Find the largest possible set perfect and return an integer, the size of that set. If no such set is possible, then return -1. It is guaranteed that all elements in onionBags are distinct.

Constraints

• 1 ≤ onionBags.length ≤ 10⁵
• 1 ≤ onionBags[i] ≤ 10⁹

Example 1

Input:

onionBags = [3, 9, 4, 2, 16]

Output:

3

Explanation: The following are the perfect sets:

• Set perfect = [3, 91]. The size of this set is 2.
• Set perfect = [4, 2]. The size of this set is 2.
• Set perfect = [4, 16]. The size of this set is 2.
• Set perfect = [4, 2, 16]. The size of this set is 3. The size of the largest set is 3. The image below illustrates the correct ordering of the purchased onion bags by count.