The Tree Root and Its Children

Problem Background

Special for beginners, ^_^

Problem Description

Given a tree, output its root root, the node max with the most children, and that node's children.

Input Format

The first line: $n$ (number of nodes $\le 100$), $m$ (number of edges $\le 200$).

The following $m$ lines each contain two nodes $x$ and $y$, meaning $y$ is a child of $x$ ($x, y \le 100$).

Output Format

The first line: the tree root: root.

The second line: the node max with the most children.

The third line: max's children.

Sample Input

8 7
4 1
4 2
1 3
1 5
2 6
2 7
2 8

Sample Output

4
2
6 7 8

Constraints

$n \le 100,\ m \le 200$.

Time limit $1$ s, memory $1024$ KiB per test case.

Hint

• The root is the only node that is never listed as a child (no parent edge points to it).
• Build the child lists, then the node whose list is longest is max.