Migrated from Lutece 931 Car race game

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Description

Bob is a game programming specialist. In his new car race game, there are some racers($n$ means the amount of racers $(1 \leq n \leq 100000)$) racers star from someplace($x_i$ means Starting point coordinate),and they possible have different speed($V$ means speed).so it possibly takes place to overtake(include staring the same point ). now he want to calculate the maximal amount of overtaking.

Input

The first line of the input contains an integer $n$-determining the number of racers. Next $n$ lines follow, each line contains two integer $X_i$ and $V_i$.($X_i$ means the $i_{th}$ racer's Starting point coordinate, $V_i$ means the ith racer's speed.$0<X_i, V_i<1000000$).

Output

For each data set in the input print on a separate line, on the standard output, the integer that represents the maximal amount of overtaking.

Samples

2
2 1
2 2
5
2 6
9 4
3 1
4 9
9 1
7
5 5
6 10
5 6
3 10
9 10
9 5
2 2

1
6
7

Resources

2011 Heilongjiang collegiate programming contest