# Problem C

H-Index

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 |