There are n points given in a space. There are no three points, such that they lie on the same straight line. Each pair of points is connected by a segment coloured red or black. Each triangle, whose sides have the same colour is called a monochromatic triangle. We are given a list of all red segments and we want to find the number of all monochromatic triangles.

Task

• reads from the text file TRO.IN the following data: the number of points, the number of red segments and their list,
• finds the number of monochromatic triangles,
• writes the result to the text file TRO.OUT.

Input

In the second line of the same file there is one integer m, 0 <= m <= 250000, which equals the number of red segments.

In each of the following m lines there are two integers p and k separated by a single space, 1 <= p < k <= n. They are numbers of vertices which are ends of a red segment.

Output

Example

6 
9
1 2
2 3
2 5
1 4
1 6
3 4
4 5
5 6
3 6

2