IMGroups

Alex has a lot of contacts in his Hyper Instant Messenger (HIM), and therefore, it takes some time to find the right contact. HIM supports Contact Groups, and each contact can be placed into a group. However, HIM's group support is rather limited. It allows for only one of the following two scenarios: 1) Multiple groups, but every contact belongs to a single group, or 2) All contacts exist only in a global contacts list (and no groups are created).

It takes Alex k seconds to find an entry in any list of k entries. If groups exist, HIM will first show a list of all the groups, and once a group is selected, a list of all contacts within that group will be displayed. If groups do not exist, HIM will simply show a single list containing all the contacts in the global list. For example, if Alex has 5 contacts in the global list, it will take 5 seconds to find any one of them. If Alex splits those contacts into two groups with 2 and 3 users each, it will first take him 2 seconds to find the right group, and then 2 or 3 seconds to find the right contact depending on which group he chooses.

You will be given an int N representing the total number of contacts. Arrange the contacts optimally (either in one global contacts list or in several groups) such that the maximal time needed to find a contact is minimized. Return this time.