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 $n$ ($1 \leq n \leq 100000$), which is the number of papers you have written.

The next $n$ lines describe the papers. Each of these lines contains a single integer $c$ ($0 \leq c \leq 1000000000$), which is the number of citations that this paper has.

-----Output-----
Display your $H$-Index.

-----Examples-----
Sample Input 1:
5
7
1
2
1
5
Sample Output 1:
2

Sample Input 2:
5
7
1
3
1
5
Sample Output 2:
3

Source: kattis | Difficulty: MEDIUM
Tags: Sorting

Divide and conquer


Solutions: