Given a weighted tree with vertices and edges, your task is to find the diameter and radius of the tree.

We say the **diameter** of the tree is the **largest distance** between any two points.

We say the **radius** of a tree is the **minimum** of the **maximum** distances for **all points**.

#### Input Specification

First line, one integer , denoting the number of vertices.

The next lines will have three integers , denoting that there is an edge between vertices and , with a weight of .

#### Output Specification

On separate lines, output the diameter, and the radius of the tree in that order.

#### Sample Input

```
5
1 2 1
2 3 2
3 4 5
2 5 7
```

#### Sample Output

```
14
7
```

#### Sample Explanation

The graph is depicted below:

We can see that the distance between node and is the greatest distance, thus is the diameter.

We can see that the minimum value between the maximum distances along the diameter are , thus is the radius.

## Comments