It is important for researchers to write many high quality academic papers. Jorge has recently discovered a way to measure how impactful a researcher's papers are: the H-index.
The H-index score of a researcher is the largest integer h such that the researcher has h papers with at least h citations each.
Jorge has written N papers in his lifetime. The i-th paper has Ai citations. The number of citations that each paper has will never change after it is written. Please help Jorge determine his H-index score after each paper he wrote.
The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing N, the number of papers Jorge wrote.
The second line contains N integers. The i-th integer is Ai, the number of citations the i-th paper has.
For each test case, output one line containing Case #x: y
, where x
is
the test case number (starting from 1) and y
is a space-separated list of
integers. The i-th integer is the H-index score after Jorge wrote his i-th
paper.
1 ≤ N ≤ 1000.
Test set 2 (Hidden)
1 ≤ N ≤ 105.
Input Output 2 3 5 1 2 Case #1: 1 1 2 6 Case #2: 1 1 2 2 2 3 1 3 3 2 2 15
In Sample Case #1, Jorge wrote N = 3 papers.
- After the 1st paper, Jorge's H-index score is 1, since he has 1 paper with at least 1 citation.
- After the 2nd paper, Jorge's H-index score is still 1.
- After the 3rd paper, Jorge's H-index score is 2, since he has 2 papers with at least 2 citations (the 1st and 3rd papers).
In Sample Case #2, Jorge wrote N = 6 papers.
- After the 1st paper, Jorge's H-index score is 1, since he has 1 paper with at least 1 citation.
- After the 2nd paper, Jorge's H-index score is still 1.
- After the 3rd paper, Jorge's H-index score is 2, since he has 2 papers with at least 2 citations (the 2nd and 3rd papers).
- After the 4th paper, Jorge's H-index score is still 2.
- After the 5th paper, Jorge's H-index score is still 2.
- After the 6th paper, Jorge's H-index score is 3, since he has 3 papers with at least 3 citations (the 2nd, 3rd and 6th papers).