Calculate the H-Index

The H-Index is a metric that attempts to measure both the productivity and citation impact of the publications of a researcher. Given a list of citation counts for each paper, the H-Index is defined as the maximum value h such that the researcher has published h papers that have each been cited at least h times.

Mathematically, this can be expressed as:

$$h = \max\{h : \text{number of papers with at least } h \text{ citations} \geq h\}$$

The input consists of several test cases. Each test case begins with an integer indicating the number of papers, followed by a line of space-separated integers representing the citation counts of the papers. The input terminates with a test case where the number of papers is 0. For each test case, output the computed H-Index on a separate line.

inputFormat

Input Format:

• Multiple test cases are provided via standard input.
• For each test case:
• The first line contains an integer n (n ≥ 0), which indicates the number of papers. A value of 0 indicates the end of input.
• The second line contains n space-separated integers representing the citation counts.
• There is no extra data after the terminating test case.

outputFormat

Output Format:

• For each test case (except the terminating case), output a single integer representing the calculated H-Index on a new line.

## sample

5
6 5 3 1 0
4
4 4 4 4
8
10 8 5 4 3 3 2 1
0

3
4
4

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