A. Cyclic Trees
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Recall that an unrooted tree of size $$$n$$$ is an undirected connected graph with $$$n - 1$$$ edges.

Given an unrooted tree of size $$$n$$$, find two nodes $$$u$$$ and $$$v$$$, such that when the undirected edge $$$(u, v)$$$ is added to the tree, a simple cycle that consists of at least $$$3$$$ nodes is created.

It can be shown that under the constraints of the problem, an answer always exists.

Input

The first line of the input consists of a single integer $$$n$$$ $$$(3 \le n \le 100)$$$, the size of the tree.

On each of the next $$$n - 1$$$ lines, there are two integers $$$u$$$, $$$v$$$ $$$(1 \le u, v \le n)$$$, representing an edge in the tree between nodes $$$u$$$ and $$$v$$$.

It is guaranteed that the input provides a valid tree.

Output

Output exactly two integers $$$u$$$ and $$$v$$$, such that when the edge $$$(u, v)$$$ is added to the tree, there is a cycle of size at least $$$3$$$.

Examples
Input
3
1 2
2 3
Output
1 3
Input
4
1 2
1 3
3 4
Output
1 4
Note

See the second example after the edge $$$(1, 4)$$$ is added:

A cycle of size $$$3$$$ that consists of nodes $$$1$$$, $$$3$$$, and $$$4$$$ is created. Another valid answer would be the edge $$$(2, 4)$$$, which would create a cycle of size $$$4$$$.