Problem 3. Job Completion

USACO 2024 December Contest, Gold

Bessie the cow has $N$ ($1\le N\le 2\cdot 10^5$) jobs for you to potentially complete. The $i$-th one, if you choose to complete it, must be started at or before time $s_i$ and takes $t_i$ time to complete ($0\le s_i\le 10^{18}, 1\le t_i\le 10^{18}$).

What is the maximum number of jobs you can complete? Time starts at $0$, and once you start a job you must work on it until it is complete, without starting any other jobs in the meantime.

INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains $T$, the number of independent test cases ($1\le T\le 10$). Each test case is formatted as follows.

The first line contains $N$.

Each of the next $N$ lines contains two integers $s_i$ and $t_i$. Row $i+1$ has the details for the $i$th job.

It is guaranteed that the sum of $N$ over all test cases does not exceed $3\cdot 10^5$.

OUTPUT FORMAT (print output to the terminal / stdout):

For each test case, the maximum number of jobs you can complete, on a new line.

SAMPLE INPUT:

3
2
1 4
1 2
2
2 3
1 2
3
1 4
2 3
1 2

SAMPLE OUTPUT:

1
2
2

For the first test case, you can only complete one of the jobs. After completing one job, it will then be time $2$ or later, so it is too late to start the other job, which must be started at time $1$ or earlier.

For the second test case, you can start the second job at time $0$ and finish at time $2$, then start the first job at time $2$ and finish at time $5$.

SCORING: Inputs 2: Within the same test case, all $t_i$ are equal.Inputs 3-4: $N\le 2000$, $s_i, t_i\le 2000$Inputs 5-8: $N\le 2000$Inputs 9-16: No additional constraints.

Problem credits: Benjamin Qi