Problem C
H-Index
![/problems/hindex/file/statement/en/img-0001.jpg](/problems/hindex/file/statement/en/img-0001.jpg)
In research, it is tough to determine how good of a researcher you are. One way that people determine how good you are is by looking at your $H$-Index.
Each paper has a certain number of citations. Your $H$-Index is the largest number $H$ such that you have $H$ papers with at least $H$ citations. Given the number of citations on each paper you have written, what is your $H$-Index?
Input
The first line of input contains a single integer $n$ ($1 \leq n \leq 100\, 000$), which is the number of papers you have written.
The next $n$ lines describe the papers. Each of these lines contains a single integer $c$ ($0 \leq c \leq 1\, 000\, 000\, 000$), which is the number of citations that this paper has.
Output
Display your $H$-Index.
Sample Input 1 | Sample Output 1 |
---|---|
5 7 1 2 1 5 |
2 |
Sample Input 2 | Sample Output 2 |
---|---|
5 7 1 3 1 5 |
3 |
Sample Input 3 | Sample Output 3 |
---|---|
3 4 2 3 |
2 |