Nested Rubber Bands

You have a tree of $n$ vertices. You are going to convert this tree into $n$ rubber bands on an infinitely large plane. The conversion follows these rules:

• For every pair of vertices $a$ and $b$, rubber bands $a$ and $b$ intersect if and only if there is an edge between $a$ and $b$ in the tree.
• Each rubber band has the shape of a simple loop. In other words, a rubber band is a loop that does not intersect itself.

We define the following terms:

• Rubber band $a$ includes rubber band $b$ if and only if rubber band $b$ lies inside the area of rubber band $a$ and the two do not intersect.
• A sequence of rubber bands $a_1, a_2, \ldots, a_k$ ($k \ge 2$) is nested if and only if for every $i$ ($2 \le i \le k$), $a_{i-1}$ includes $a_i$.

This is an example of a conversion. Rubber bands $5$ and $6$ are nested.

It can be proved that a conversion and a nested sequence of rubber bands satisfying the constraints always exist.

What is the maximum length of a nested sequence of rubber bands that can be obtained from the given tree? Find it and print it.

The first line contains an integer $n$ ($3 \le n \le 10^{5}$), the number of vertices in the tree.

The $i$-th of the next $n-1$ lines contains two integers $a_i$ and $b_i$ ($1 \le a_i \lt b_i \le n$), meaning there is an edge between $a_i$ and $b_i$. The given graph is guaranteed to be a tree on $n$ vertices.

Print the answer.

In the first input, you can obtain a nested sequence of $4$ rubber bands ($1$, $2$, $5$, and $6$) with the conversion shown below. Other conversions also produce a nested sequence of $4$ rubber bands. However, no nested sequence of $5$ or more rubber bands can be made from this tree.

One possible conversion for the second input is shown below.