Problem Description

Given an undirected graph \( G \) with \( N \) vertices and \( M \) edges. The vertices of \( G \) are numbered from \( 1 \) to \( N \), and the \( i \)-th edge ( \( 1 \leq i \leq M \) ) connects vertices \( a_i \) and \( b_i \). \( G \) does not have self-loops or multiple edges.

You can repeatedly add edges between two vertices of \( G \), but the resulting graph must not have self-loops or multiple edges. Also, if vertices \( 1 \) and \( 2 \) are connected directly or indirectly, you will be struck by a voltage of \( 1000000007 \) volts. This must be avoided.

Under these conditions, what is the maximum number of edges you can add? Note that vertices \( 1 \) and \( 2 \) are not connected directly or indirectly initially.

Input Format

The input is given from the standard input in the following format:

\( N \) \( M \) \( a_1 \) \( b_1 \) \( : \) \( a_M \) \( b_M \)

Output Format

Output the maximum number of edges that can be added.

Sample Input and Output

Sample Input #1

4 1
1 3

Sample Output #1

2

Sample Input #2

2 0

Sample Output #2

0

Sample Input #3

9 6
1 4
1 8
2 5
3 6
4 8
5 7

Sample Output #3

12

Notes/Hints

Constraints

• \( 2 \leq N \leq 10^5 \)
• \( 0 \leq M \leq 10^5 \)
• \( 1 \leq a_i < b_i \leq N \)
• All pairs \( (a_i, b_i) \) are distinct.
• Vertices \( 1 \) and \( 2 \) are not connected directly or indirectly in \( G \).

Sample Explanation 1

As shown in the figure, you can add 2 edges. Adding more than 3 edges is not possible.

Sample Explanation 2

No edges can be added.

见题面 Input 部分

见题面 Output 部分