CSES - Tree Diameter
• Time limit: 1.00 s
• Memory limit: 512 MB
You are given a tree consisting 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 describing 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
• $1 \le n \le 2 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5 1 2 1 3 3 4 3 5

Output:
3

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