Analyzing Polyline

题意翻译

给定n个函数 y=max(0, kx+b)中的k和b的值，将所有这些（被截断的一次）函数相加得到一个新的函数，求这个新函数的图像中有多少个拐点 数据范围见原题

题目描述

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:  Let's define a sum of $ n $ functions $ y_{1}(x),...,y_{n}(x) $ of the given type as function $ s(x)=y_{1}(x)+...+y_{n}(x) $ for any $ x $ . It's easy to show that in this case the graph $ s(x) $ is a polyline. You are given $ n $ functions of the given type, your task is to find the number of angles that do not equal 180 degrees, in the graph $ s(x) $ , that is the sum of the given functions.Valeric and Valerko really want to watch the next Euro Championship game, so they asked you to help them.

输入输出格式

输入格式

The first line contains integer $ n $ $ (1<=n<=10^{5}) $ — the number of functions. Each of the following $ n $ lines contains two space-separated integer numbers $ k_{i},b_{i} $ $ (-10^{9}<=k_{i},b_{i}<=10^{9}) $ that determine the $ i $ -th function.

输出格式

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.

输入输出样例

输入样例 #1

1
1 0

输出样例 #1

1

输入样例 #2

3
1 0
0 2
-1 1

输出样例 #2

2

输入样例 #3

3
-2 -4
1 7
-5 1

输出样例 #3

3