Edge Weight Assignment

Description:

Input:

The first line contains integer $$$n$$$ ($$$3 \le n \le 10^{5}$$$) — the number of vertices in given tree.

The $$$i$$$-th of the next $$$n-1$$$ lines contains two integers $$$a_{i}$$$ and $$$b_{i}$$$ ($$$1 \le a_{i} \lt b_{i} \le n$$$) — it means there is an edge between $$$a_{i}$$$ and $$$b_{i}$$$. It is guaranteed that given graph forms tree of $$$n$$$ vertices.

Output:

Print two integers — the minimum and maximum possible value of $$$f$$$ can be made from valid assignment of given tree. Note that it's always possible to make an assignment under given constraints.

Sample Input:

6
1 3
2 3
3 4
4 5
5 6

Sample Output:

1 4

Sample Input:

6
1 3
2 3
3 4
4 5
4 6

Sample Output:

3 3

Sample Input:

7
1 2
2 7
3 4
4 7
5 6
6 7

Sample Output:

1 6

Note:

In the first example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum.

In the second example, possible assignments for each minimum and maximum are described in picture below. The $$$f$$$ value of valid assignment of this tree is always $$$3$$$.

In the third example, possible assignments for each minimum and maximum are described in picture below. Of course, there are multiple possible assignments for each minimum and maximum.