Longest Path in a Planetary Tree

You are given a hierarchy of planets forming a tree structure. Each directed edge represents a wormhole from one planet to another. Planet 1 is the root of the tree, and you need to find the maximum number of wormholes that can be traversed from Planet 1 to any other planet.

The problem can be formulated as follows:

where $d(1,v)$ is the number of edges from Planet 1 to planet $v$.

Input Format: The first line contains an integer $N$ representing the number of planets. For $N > 1$, the next $N-1$ lines each contain two space-separated integers $u$ and $v$, which denote a wormhole from planet $u$ to planet $v$.

Output Format: Output a single integer indicating the length of the longest path starting from Planet 1.

inputFormat

The input is provided via standard input.

The first line contains an integer $N$, the number of planets. For $N > 1$, the following $N-1$ lines each contain two integers $u$ and $v$, representing a directed edge (wormhole) from planet $u$ to planet $v$.

outputFormat

Output a single integer to standard output, which is the length of the longest path from planet 1 in the given tree structure.## sample

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