The Right Triangles

A student is given a list of N triangles. Each triangle is identfied by the coordinates of its three corners in the 2-D cartesian plane. His job is to figure out how many of the given triangles are right triangles. A right triangle is a triangle in which one angle is a 90 degree angle. The vertices of the triangles have integer coordinates and all the triangles given are valid( three points aren't colinear ).
        
       Input:-5
0 5 19 5 0 0
17 19 12 16 19 0
5 14 6 13 8 7
0 4 0 14 3 14
0 2 0 14 9 2
       Input Description: The first line of the input contains an integer N denoting the number of triangles. Each of the following N lines contain six space separated integers x1 y1 x2 y2 x3 y3 where (x1, y1), (x2, y2) and (x3, y3) are the vertices of a triangle. 
       Output: 3
       Output Description: Output one integer, the number of right triangles among the given triangles.
 
       Constraints: 1 <= N <= 100000 (105)
0 <= x1, y1, x2, y2, x3, y3 <= 20
       Explanation: The first triangle and the last two triangles of the example are right triangles.