H-Index

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Time limit1sMemory limit256 MB

Summary

Given N citation counts, compute the largest H with at least H papers cited at least H times.

Level: Easy3 of 10
Topics: Sorting
Solved: No attempts yet

Problem

How do you measure a scientist's success? You can count the papers they published, or you can count the impact of those papers, that is, how often other scientists cite them. Both numbers matter. A paper has citation score $C$ if other scientists cited it $C$ times in their own papers. The h-index is one metric that reflects the number of papers and their citation scores at the same time.

The h-index is the largest integer $H$ with the following property: the scientist can choose $H$ papers whose citation score is at least $H$ . For example, if a scientist wrote 10 papers and each of them was cited 10 or more times, that scientist's h-index is at least 10.

Given the citation scores of every paper a scientist wrote, write a program that computes the h-index.

Input

The first line contains the number of papers $N$ ( $1 \le N \le 500{,}000$ ).

The second line contains $N$ citation scores separated by spaces. Each citation score is an integer between $0$ and $1{,}000{,}000$ .

Output

Print the h-index on the first line.

Hint

In the first example two papers have a citation score of 2 or more, the one cited 4 times and the one cited 8 times. Only one paper has a citation score of 3 or more, so the h-index is 2.

Examples2

Example 1
Input
```
5
1 1 4 8 1
```
Expected output
```
2
```
Example 2
Input
```
5
8 5 3 4 10
```
Expected output
```
4
```