+ محدودیت زمان: ۴ ثانیه + محدودیت حافظه: ۳۲ مگابایت ---------- In a two-dimensional coordinate plane, there are N distinct points given as input, specified by their coordinates $(x_i, y_i)$ for $i = 1, 2, ..., N$. Your task is to develop a program that computes the number of unique Orthogonal (right) triangles that can be formed by selecting any three of the provided points. An Orthogonal triangle is a triangle in which one of the angles measures exactly 90 degrees. # Input The first line of input contains an integer N, the number of points. Each of the following N lines contains the coordinates of one point, two integers $(x_i, y_i)$ separated by a space. No two points will be located at the same coordinates. # Output Output the number of Orthogonal triangles. # Constrints * $3 \leq N \leq 1500 $ * $-10^9 \leq x_i,y_i \leq 10^9 $ # Sample Test Data ## input 1 ``` 5 1 1 1 0 0 0 -1 0 -1 1 ``` ## input 2 ``` 7 ```