Problem Description

Given a binary tree and a starting node, calculate the minimum time to burn the entire tree. Fire spreads from the starting node to all connected nodes (parent and children) each second. Return the total time needed.

Input Format

First line: n (number of nodes). Second line: starting node value. Next n-1 lines: parent-child relationships as "parent child".

Output Format

Minimum time in seconds to burn the entire tree.

Constraints

• 1 ≤ n ≤ 1000

• Node values are unique integers 1 to n

• Tree is connected (n-1 edges)

• Fire spreads to adjacent nodes each second

• Starting node burns at time 0

Sample Input/Output

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

3

Explanation

Tree structure with start=3: Fire spreads from 3 to 1,6,7 (time 1), then to 2 (time 2), then to 4,5 (time 3). Total time: 3.