Problem Statement

The republic of AtCoder has N cities numbered 1 through N and M roads numbered 1 through M.
Road i leads from City A_i to City B_i, but you cannot use it to get from City B_i to City A_i.
Puma is planning her journey where she starts at some city, travels along zero or more roads, and finishes at some city.
How many pairs of cities can be the origin and destination of Puma's journey? We distinguish pairs with the same set of cities in different orders.

Input

Input is given from Standard Input in the following format:
N M
A_1 B_1
$\vdots$
A_M B_M

Output

Print the answer.

Constraints

• $2 \leq N \leq 2000$
• $0 \leq M \leq \min(2000,N(N-1))$
• $1 \leq A_i,B_i \leq N$
• $A_i \neq B_i$
• (A_i,B_i) are distinct.
• All values in input are integers.

Sample Input 1

3 3
1 2
2 3
3 2

Sample Output 1

7

We have seven pairs of cities that can be the origin and destination: (1,1),(1,2),(1,3),(2,2),(2,3),(3,2),(3,3).

Sample Input 2

3 0

Sample Output 2

3

We have three pairs of cities that can be the origin and destination: (1,1),(2,2),(3,3).

Sample Input 3

4 4
1 2
2 3
3 4
4 1

Sample Output 3

16

Every pair of cities can be the origin and destination.

见题面 Input 部分

见题面 Output 部分