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 $2 \rightarrow 1 \rightarrow 3 \rightarrow 5$.