Job Completion
Bessie the cow has N (1≤N≤2⋅105) jobs for you to potentially complete. The i-th one, if you choose to complete it, must be started at or before time si and takes ti time to complete (0≤si≤1018,1≤ti≤1018).
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.
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 ti are equal.
- Inputs 3-4: N≤2000, si,ti≤2000
- Inputs 5-8: N≤2000
- Inputs 9-16: No additional constraints.
Problem credits: Benjamin Qi
Source: USA Computing Olympiad.
Input Format
The first line contains T, the number of independent test cases (1≤T≤10). Each test case is formatted as follows.
The first line contains N.
Each of the next N lines contains two integers si and ti. Row i+1 has the details for the ith job.
It is guaranteed that the sum of N over all test cases does not exceed 3⋅105.
Output Format
For each test case, the maximum number of jobs you can complete, on a new line.