A company has n employees, numbered 1 through n, and m collaboration links. Each link connects two employees, and collaboration is mutual. Two employees are reachable from each other if a chain of collaboration links connects them.

Count the number of unordered pairs {i, j} with i != j such that i and j are reachable from each other.

Input format

• Line 1: two integers n and m.
• Next m lines: two integers u and v (1-indexed, u != v), a collaboration link.

Output format

A single integer: the number of reachable unordered pairs.

Constraints

• 1 <= n <= 100000
• 0 <= m <= 200000
• 1 <= u, v <= n and u != v

5 3
1 2
2 3
4 5

4

4 0

0