P16744 [GKS 2019 #H] H-index

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 $A_i$ 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 $A_i$, 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.

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). ### Limits $1 \le T \le 100$. $1 \le A_i \le 10^5$. **Test set 1 (Visible)** $1 \le N \le 1000$. **Test set 2 (Hidden)** $1 \le N \le 10^5$.