Math Lessons
All LKSH students are well aware that the Maya Indians were quite advanced, necessitating a method to pass their knowledge from one generation to the next. Consequently, the young boys and girls of the Maya tribes attended schools similar to modern-day children. In these schools, they studied simpler subjects. For instance, the Indian Melkinchuk faced a geometry problem in his final exam. However, due to spending more time riding horses and visiting the beach instead of attending school, Melkinchuk was unable to solve it.
The last topic Kolya studied in school was the slope of line segments on a plane. The slope of a segment connecting the points ((x_1, y_1)) and ((x_2, y_2)) was defined by the Indians as the ratio ((y_2 - y_1)/(x_2 - x_1)). Melkinchuk's task was to identify two points from the given ones on the plane that form a segment with the maximum slope. This is the problem you need to solve.
Input
The first line of the input contains the number (N) ((2 N 100,000))—the number of points in the problem. The following (N) lines each contain the coordinates of a point on the plane, given as integers (x_i) and (y_i), separated by a space. These integers do not exceed (10^9) in absolute value. It is guaranteed that no two points have the same (x)-coordinate.
Output
The output should consist of two numbers—the indices of the two points that form the segment with the greatest slope. The points in the input are numbered starting from one. If there are multiple solutions, you may output any one of them.