Description

A data center has N servers with network connections between them. We want to find servers farthest from the main server (server 1). Distance is measured by minimum hops (number of connections traversed). Find the count of servers farthest from server 1.

Input

Output

Constraints

• •2 <= N <= 20,000
• •1 <= edges <= 50,000
• •Graph is connected

Examples

6, [[3,6], [4,3], [3,2], [1,3], [1,2], [2,4], [5,2]]

3