H-Index

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.

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 $1{,}000{,}000$.

Print the h-index on the first line.

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.