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 a connection 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 diameter.

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

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