Two Points with the Greatest Slope

You are given $N$ distinct points on a plane. All x-coordinates are distinct, and all y-coordinates are distinct.

For two points $(x_1, y_1)$ and $(x_2, y_2)$, the absolute value of the slope of the line passing through them is

$$\left|\frac{y_2-y_1}{x_2-x_1}\right|$$

Write a program that finds the two point numbers whose absolute slope is as large as possible.

The first line contains the number of points $N$. $(2 \le N \le 50,000)$

Each of the next $N$ lines contains the x-coordinate and y-coordinate of one point, separated by a space. Every coordinate is an integer with absolute value at most 30,000. The points are numbered from 1 to $N$ in input order.

Print the numbers $A$ and $B$ of the two points with the greatest absolute slope, separated by a space. Print them so that $A < B$.

If more than one pair satisfies the condition, print the pair with the smallest $A$. If there is still more than one such pair, print the one with the smallest $B$.