2018 Rocky Mountain Regional Contest

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2018-11-03 16:00 UTC

2018 Rocky Mountain Regional Contest

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2018-11-03 21:00 UTC
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Problem D
H-Index

/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