Score : $1400$ points

Problem Statement

There are $N$ turkeys. We number them from $1$ through $N$.

$M$ men will visit here one by one. The $i$-th man to visit will take the following action:

• If both turkeys $x_i$ and $y_i$ are alive: selects one of them with equal probability, then eats it.
• If either turkey $x_i$ or $y_i$ is alive (but not both): eats the alive one.
• If neither turkey $x_i$ nor $y_i$ is alive: does nothing.

Find the number of pairs $(i,\ j)$ ($1 \leq i < j \leq N$) such that the following condition is held:

• The probability of both turkeys $i$ and $j$ being alive after all the men took actions, is greater than $0$.

Constraints

• $2 \leq N \leq 400$
• $1 \leq M \leq 10^5$
• $1 \leq x_i < y_i \leq N$

Input

Input is given from Standard Input in the following format:

$N$ $M$

$x_1$ $y_1$

$x_2$ $y_2$

$:$

$x_M$ $y_M$

Output

Print the number of pairs $(i,\ j)$ ($1 \leq i < j \leq N$) such that the condition is held.

3 1
1 2

2

$(i,\ j) = (1,\ 3), (2,\ 3)$ satisfy the condition.

4 3
1 2
3 4
2 3

1

$(i,\ j) = (1,\ 4)$ satisfies the condition. Both turkeys $1$ and $4$ are alive if:

• The first man eats turkey $2$.
• The second man eats turkey $3$.
• The third man does nothing.

3 2
1 2
1 2

0

10 10
8 9
2 8
4 6
4 9
7 8
2 8
1 8
3 4
3 4
2 7

5