Description

Given a sequence, please find the largest integer $H$ such that in the original sequence there are at least $H$ numbers $\ge H$.

Input Format

The first line contains a positive integer $N$, which denotes the number of elements in the sequence.

The second line contains $N$ integers $A_i$, which denote the elements of the sequence.

Output Format

Output one line containing an integer $H$, which is the largest integer that satisfies the condition.

5
1 1 4 8 1 

2

5
8 5 3 4 10

4

Hint

Sample Explanation #1.

There are $2$ numbers greater than or equal to $2$, namely $4$ and $8$.

Sample Explanation #2.

There are $4$ numbers greater than or equal to $4$, namely $8$, $5$, $4$, and $10$.

Constraints.

For $100\%$ of the testdata, $1\le N\le 5\times 10^5$, $0\le A_i\le 1\times 10^6$.

Notes.

The score of this problem follows the original COCI settings, with a full score of $50$.

Translated from COCI2016_2017 CONTEST #6 T1 HINDEKS.

Translated by ChatGPT 5