Problem Description

For the binary tree shown below, its depth, width, and distances between nodes are as follows:

• Depth: $4$.
• Width: $4$.
• The distance between nodes 8 and 6: $8$.
• The distance between nodes 7 and 6: $3$.

Here, the width is the maximum number of nodes on the same level of the binary tree. The distance between nodes $u$ and $v$ is defined as twice the number of edges directed toward the root plus the number of edges directed toward the leaves, along the shortest directed path from $u$ to $v$.

Given a binary tree rooted at node 1, compute its depth, width, and the distance between two specified nodes $x, y$.

Input Format

The first line contains an integer $n$, the number of nodes in the tree.
The next $n - 1$ lines each contain two integers $u, v$, indicating that there is an edge connecting $u$ and $v$ in the tree.
The last line contains two integers $x, y$, asking for the distance between $x$ and $y$.

Output Format

Output three lines, each containing one integer, representing the depth, the width, and the distance between $x$ and $y$, in this order.

10                                
1 2                            
1 3                            
2 4
2 5
3 6
3 7
5 8
5 9
6 10
8 6

4
4
8

Hint

For all test points, $1 \leq u, v, x, y \leq n \leq 100$, and the input describes a tree. It is guaranteed that $u$ is the parent of $v$.

Translated by ChatGPT 5