Problem Statement

We have a grid with N rows and N columns.
The cell at the i-th row and j-th column is denoted (i, j).
Initially, M of the cells are painted black, and all other cells are white.
Specifically, the cells (a_1, b_1), (a_2, b_2), ..., (a_M, b_M) are painted black.
Snuke will try to paint as many white cells black as possible, according to the following rule:

• If two cells (x, y) and (y, z) are both black and a cell (z, x) is white for integers 1≤x,y,z≤N, paint the cell (z, x) black.

Find the number of black cells when no more white cells can be painted black.

Input

The input is given from Standard Input in the following format:
N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of black cells when no more white cells can be painted black.

Constraints

• 1≤N≤10^5
• 1≤M≤10^5
• 1≤a_i,b_i≤N
• All pairs (a_i, b_i) are distinct.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

3

It is possible to paint one white cell black, as follows:

• Since cells (1, 2) and (2, 3) are both black and a cell (3, 1) is white, paint the cell (3, 1) black.

Sample Input 2

2 2
1 1
1 2

Sample Output 2

4

It is possible to paint two white cells black, as follows:

• Since cells (1, 1) and (1, 2) are both black and a cell (2, 1) is white, paint the cell (2, 1) black.
• Since cells (2, 1) and (1, 2) are both black and a cell (2, 2) is white, paint the cell (2, 2) black.

Sample Input 3

4 3
1 2
1 3
4 4

Sample Output 3

3

No white cells can be painted black.

见题面 Input 部分

见题面 Output 部分