Shil decided to go for hill climbing on this weekend, but he doesn't have the map of all the hills. However, he's smart enough to make his own map.

There are N hills arranged on a line, each in the form of a vertical line segment with one endpoint on the ground. The hills are numbered with numbers from 1 to N from left to right. The i^th hill stands at the position x_i with its top at height y_i.

A pair (a, b) ( where a < b ) is called beautiful if and only if Shil will be able to see the peak of b^th hill standing on the top of a^th hill.

In order to make his own map, Shil needs total number of beautiful pairs. As Shil is not a very good programmer, he asks for your help.

Assume that Shil's height is very small as compared to the height of hills. (Really!) Thus, we can assume that Shil's eyes are exactly at the height of peak if he is standing at peak of some hill.

You can also assume that Shil is able to see peak of certain hills if distance between peak and Shil's sight is less than 10^-4.

Input format:
The first line of the input contains a single integer N , the number of hills. The next N lines describe the hills. The i^th of them contains two space-separated integers x_i, y_i , the position and the height of the i^th hill. The hills are given in the ascending order of x_i, i.e., x_i < x_j for i < j.

Output format:
Print the total number of beautiful pairs.

Constraints:
2 ≤ N ≤ 1000
1 ≤ x_i , y_i ≤ 10⁹