Where to Put the Server

A company's n offices, numbered 0 to n - 1, are linked by the n - 1 two-way cables in cables, each a pair [a, b], so that there is exactly one route between any two offices: the network is a tree. The main server will go in one office. A message from the server crosses some number of cables to reach each office, and the server's delay is the largest of these numbers.

Write best_roots(n, cables) that returns a sorted list of every office where the server's delay would be as small as possible. In tree words, these are the roots that give the tree its smallest height.

Examples

best_roots(4, [[1, 0], [1, 2], [1, 3]])  # returns [1]
best_roots(6, [[3, 0], [3, 1], [3, 2], [3, 4], [5, 4]])  # returns [3, 4]
best_roots(1, [])  # returns [0]

In the second network, a server in office 3 or office 4 reaches every office within 2 cables, while from any other office some office is 3 cables away.

Constraints

• 1 <= n <= 20,000, and the cables always form a tree.

Note

• The tree can be a single chain of 20,000 offices. Python stops recursion at about 1,000 levels, so a recursive search has to be rewritten with a stack of your own.