Largest Distance between nodes of a Tree

Given an arbitrary unweighted rooted tree which consists of N nodes.

The goal of the problem is to find largest distance between two nodes in a tree.

Distance between two nodes is a number of edges on a path between the nodes (there will be a unique path between any pair of nodes since it is a tree).

The nodes will be numbered 0 through N - 1.

The tree is given as an array A, there is an edge between nodes A[i] and i (0 <= i < N). Exactly one of the i's will have A[i] equal to -1, it will be root node.

1 <= N <= 40000

First and only argument is an integer array A of size N.

Return a single integer denoting the largest distance between two nodes in a tree.

Input 1:

 A = [-1, 0, 0, 0, 3]

Output 1:

 3

Explanation 1:

 node 0 is the root and the whole tree looks like this: 
          0
       /  |  \
      1   2   3
               \
                4

 One of the longest path is 1 -> 0 -> 3 -> 4 and its length is 3, thus the answer is 3.