CSES Problem Set

# Tree Diameter

CSES - Tree DiameterCSES - Tree Diameter

 Time limit: 1.00 s Memory limit: 512 MB

You are given a tree that consists of $n$ nodes.

The diameter of a tree is the maximum distance between two nodes. Your task is to determine the diameter of the tree.

Input

The first input line contains an integer $n$: the number of nodes. The nodes are numbered $1,2,\ldots,n$.

Then there are $n-1$ lines that describe the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Output

Print one integer: the diameter of the tree.

Constraints
• $1 \le n \le 5 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5 1 2 1 3 3 4 3 5

Output:
3

Explanation: The diameter corresponds to the path $2 \rightarrow 1 \rightarrow 3 \rightarrow 5$.