H-index | cho.sh

문제

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.

입력

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.

출력

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.

제한

1 ≤ T ≤ 100.
1 ≤ Ai ≤ 105.

힌트

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).