Analyzing Polyline
Description
As Valeric and Valerko were watching one of the last Euro Championship games in a sports bar, they broke a mug. Of course, the guys paid for it but the barman said that he will let them watch football in his bar only if they help his son complete a programming task. The task goes like that.
Let's consider a set of functions of the following form:
Valeric and Valerko really want to watch the next Euro Championship game, so they asked you to help them.
The first line contains integer n (1 ≤ n ≤ 105) — the number of functions. Each of the following n lines contains two space-separated integer numbers ki, bi ( - 109 ≤ ki, bi ≤ 109) that determine the i-th function.
Print a single number — the number of angles that do not equal 180 degrees in the graph of the polyline that equals the sum of the given functions.
Input
The first line contains integer n (1 ≤ n ≤ 105) — the number of functions. Each of the following n lines contains two space-separated integer numbers ki, bi ( - 109 ≤ ki, bi ≤ 109) that determine the i-th function.
Output
Print a single number — the number of angles that do not equal 180 degrees in the graph of the polyline that equals the sum of the given functions.
1<br>1 0<br>
3<br>1 0<br>0 2<br>-1 1<br>
3<br>-2 -4<br>1 7<br>-5 1<br>
1<br>
2<br>
3<br>