There are $n$ points given on a plane. We are interested in the number of right-angled triangles whose vertices are among the given points and whose area belongs to the interval $[A, B]$.

Input

The first line contains three integers $n, A, B$ ($1 \le n \le 2000$, $1 \le A \le B \le 10^{18}$). The next $n$ lines describe the individual points. The $i$-th of these lines contains two integers $x_i, y_i$ ($-10^9 \le x_i, y_i \le 10^9$), which are the coordinates of the $i$-th point. The points provided in the input are distinct.

Output

The only line of output should contain the number of right-angled triangles with vertices at the given points and an area in the interval $[A, B]$.

Examples

Input 1

7 5 25
0 0
2 0
0 2
10 0
0 10
3 3
3 -3

Output 1

3