Number of Operations to Make Network Connected

There are n computers numbered from 0 to n - 1 connected by ethernet cables connections forming a network where connections[i] = [ai, bi] represents a connection between computers ai and bi. Any computer can reach any other computer directly or indirectly through the network.

You can extract certain cables between two directly connected computers, and place them between any pair of disconnected computers to make them directly connected.

Return the minimum number of times you need to do this in order to make all the computers connected. If it is not possible, return -1.

Examples

Example 1:

Input: n = 4, connections = [[0,1],[0,2],[1,2]]

Output: 1

Explanation: Remove cable between 0 and 2, place between 2 and 3.

Example 2:

Input: n = 6, connections = [[0,1],[0,2],[0,3],[1,2],[1,3]]

Output: 2

Explanation: Two extra cables exist; use them to connect components containing 4 and 5.

Example 3:

Input: n = 6, connections = [[0,1],[0,2],[0,3],[1,2]]

Output: -1

Explanation: Only 4 cables but need at least 5 to connect 6 computers.

Constraints

• 1 <= n <= 10^5
• 1 <= connections.length <= min(n * (n - 1) / 2, 10^5)
• connections[i].length == 2
• 0 <= ai, bi < n
• ai != bi
• There are no repeated connections