# Colorful Rainbows

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

## Description

Evelyn likes drawing very much. Today, she draws lots of rainbows on white paper of infinite size, each using a different color. Since there're too many rainbows now, she wonders, how many of them can be seen? For simplicity, each rainbow Li is represented as a non-vertical line specified by the equation: y=aix+bi. A rainbow Li can be seen if there exists some x-coordinate x0 at which, its y-coordinate is strictly greater than y-coordinates of any other rainbows: aix0+bi > ajx0+bj for all j != i. Now, your task is, given the set of rainbows drawn, figure out the number of rainbows that can be seen.

## Input

Standard input will contain multiple test cases. The first line of the input is a single integer T (1 <= T <= 60) which is the number of test cases. And it will be followed by T consecutive test cases. There's a blank line before every case. In each test case, there will first be an integer n (1 <= n <= 5000), which is the number of rainbows. Then n consecutive real number pairs follow. Each pair contains two real numbers, ai and bi, representing rainbow Li: y=aix+bi. No two rainbows will be the same, that is to say, have the same a and b.

## Output

Results should be directed to standard output. The output of each test case should be a single integer, which is the number of rainbows that can be seen.

## Sample Input

2

1
1 1

3
1 0
2 0
3 0

## Sample Output

1
2

None

## Source

The 5th Zhejiang Provincial Collegiate Progra