The Ironspire Crafting Guild tracks every member's direct mentor. A member may have no mentor (a founding member) or exactly one direct mentor, and any member may in turn mentor any number of other members directly. The guild masters want to recognize master mentors: members who personally (directly, not through a chain of mentorship) mentor at least 5 apprentices.

Given the full roster, print the names of all master mentors.

Input format

• Line 1: a single integer n, the number of guild members.
• Each of the next n lines contains id name mentorId, describing one member: a unique integer id, a name, and the id of that member's direct mentor, or -1 if the member has no mentor.

Output format

Print the names of all master mentors (members who are the direct mentor of at least 5 other members), one per line, sorted alphabetically in ascending order. If no member qualifies, print nothing.

Constraints

• 1 <= n <= 20000
• 1 <= id <= 200000, and all ids are distinct
• mentorId is either -1 or the id of some other member appearing in the roster (a member is never their own mentor)
• name consists of 1 to 20 lowercase and uppercase English letters, and all names are distinct

6
1 Alice -1
2 Bob 1
3 Cara 1
4 Dana 1
5 Eli 1
6 Finn 1

Alice

7
1 Gia -1
2 Hank -1
3 Ivy 2
4 Jai 2
5 Kim 2
6 Leo 2
7 Moe 1

(empty)