### Problem Statement

You are given a tree with $N$ vertices numbered $1$ through $N$. The $i$-th edge connects vertex $A_i$ and vertex $B_i$.

Find the minimum integer $K$ such that you can paint each vertex in a color so that the following two conditions are satisfied. You may use any number of colors.

-   For each color, the set of vertices painted in the color is connected and forms a simple path.
-   For all simple paths on the tree, there are at most $K$ distinct colors of the vertices in the path.

### Input

The input is given from Standard Input in the following format:

```
$N$
$A_1$ $B_1$
$\vdots$
$A_{N-1}$ $B_{N-1}$
```

### Output

Print the answer.

### Constraints

-   $1 \leq N \leq 2 \times 10^5$
-   $1 \leq A_i, B_i \leq N$
-   The given graph is a tree.
-   All values in the input are integers.

3

If K=3, the conditions can be satisfied by painting vertices 1,2,3,4, and 5 in color 1, vertex 6 in color 2, and vertex 7 in color 3. If K≤2, there is no way to paint the vertices to satisfy the conditions, so the answer is 3.