题目描述

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.

输入格式

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.

输出格式

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.

2
3
5 1 2
6
1 3 3 2 2 15

Case #1: 1 1 2
Case #2: 1 1 2 2 2 3

提示

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)

$1 \le N \le 10^5$.