Operations to Connect the Network

n computers (0 to n - 1) are joined by cables connections ([a, b]). In one operation you can take a cable between two directly connected computers and use it to join any two computers instead. Return the fewest operations to make all computers connected, or -1 if it is impossible.

For n = 4 and connections = [[0, 1], [0, 2], [1, 2]] the answer is 1.

Examples

Example 1

Input:

make_connected(4, [[0, 1], [0, 2], [1, 2]])

Output:

1

Example 2

Input:

make_connected(6, [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3]])

Output:

2

Constraints

• 1 <= n <= 100000
• 0 <= len(connections) <= 200000