LogiQuest

435. H-Index

MediumSorting

citations[i] is the citation count of paper i. Print the h-index: the largest h such that h papers have at least h citations each.

Input format

Line 1: n Line 2: n citation counts

Output format

The h-index.

Example 1

Input

5
3 0 6 1 5

Output

3

Example 2

Input

3
1 3 1

Output

1

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 6 test cases, most of them hidden.

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