Poor Turkeys

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.

Examples

Input

3 1 1 2

Output

2

Input

4 3 1 2 3 4 2 3

Output

1

Input

3 2 1 2 1 2

Output

0

Input

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

Output

5

inputFormat

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

outputFormat

Output

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

Examples

Input

3 1 1 2

Output

2

Input

4 3 1 2 3 4 2 3

Output

1

Input

3 2 1 2 1 2

Output

0

Input

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

Output

5

样例

3 2
1 2
1 2

0