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Largest Distance between nodes of a Tree


Problem Setter: ulugbek_adilbekov Problem Tester: raghav_aggiwal

Problem Description

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.



Problem Constraints

1 <= N <= 40000



Input Format

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



Output Format

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



Example Input

Input 1:

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



Example Output

Output 1:

 3



Example Explanation

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.



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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