**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.