The princess of Centauri Prime is the galaxy’s most eligible bachelorette of the year. She has hopeful
grooms lined up in front of the royal palace for a chance to spend 5 minutes to try and impress her.
After 5 minutes, the gentleman is carried out of the royal chambers by the palace guards, and the
princess makes a decision. She rates the lad on his lineage and charm by giving him a score for each of
the two properties. On Centauri Prime, low scores are better than high scores.
Suppose that she observes two gentlemen - A and B. She assigns A the scores LA and CA (for
lineage and charm, respectively). B receives scores LB and CB. Then A is dominated by B if either
• LB < LA and CB ≤ CA, or
• LB ≤ LA and CB < CA.
In other words, if at least one of B’s scores is better than A’s, and the other score is not worse. She
considers a gentleman to be efficient (or Pareto-optimal) if she has not yet met any other gentleman who
dominates him. She maintains a list of efficient grooms and updates it after each 5-minute presentation.
Given the queue of bachelors and the scores assigned to them by the princess, determine the number
of entries in the list of efficient grooms after each performance.

The first line of input gives the number of cases, N (0 < N < 40). N test cases follow.
Each one starts with a line containing n (0 ≤ n ≤ 15000) — the size of the queue. The next n lines
will each contain two scores (integers in the range [0, 10^9]). Initially, the list is empty.

For each test case, output one line containing ‘Case #x:’ followed by n lines, line i containing the size
of the list of efficient grooms after the i-th update. Print an empty line between test cases.

4
1
100 200
2
100 200
101 202
2
100 200
200 100
5
11 20
20 10
20 10
100 20
1 1

Case #1:
1

Case #2:
1
1

Case #3:
1
2

Case #4:
1
2
3
3
1

UVA11020