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 ≤ i < j ≤ 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 ≤ N ≤ 400
  • 1 ≤ M ≤ 10^5
  • 1 ≤ x_i < y_i ≤ 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 ≤ i < j ≤ N) such that the condition is held.

Sample Input 1

3 1
1 2

Sample Output 1

2

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

Sample Input 2

4 3
1 2
3 4
2 3

Sample Output 2

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.

Sample Input 3

3 2
1 2
1 2

Sample Output 3

0

Sample Input 4

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

Sample Output 4

5