How do we evaluate the success of a scientist? By the number of published papers or by their impact - more precisely, the number of citations? Both elements matter. We say that a scientific paper has a citation score if other scientists cited the paper in question in their paper (referred to it) a total of
times. One of the possible metrics of the success of scientists is their h-index that takes into account both the amount of papers and their citation scores.
A scientist's h-index is defined as the largest number with the following properties: the scientist can choose
papers such that their citation score is at least
. For example, if a scientist wrote
papers such that each of them has been cited
or more times, their h-index is (at least)
.
Write a programme that inputs the citation scores of all papers of a given scientist and outputs their h-index.
Input Specification
The first line of input contains the positive integer
, the number of papers of a given scientist.
The following line contains non-negative integers from the interval
, the citation scores of the respective papers.
Output Specification
The first and only line of output must contain the required h-index.
Sample Input 1
5
1 1 4 8 1
Sample Output 1
2
Explanation for Sample Output 1
The scientist has two papers with citation scores larger than or equal to (the papers with citation scores
and
).
Sample Input 2
5
8 5 3 4 10
Sample Output 2
4
Explanation for Sample Output 2
The scientist has four papers with citation scores larger than or equal to (the papers with citation scores
,
,
and
).
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