A12631 | Polycarp Training

Polycarp wants to train before another programming competition. During the first day of his training he should solve exactly $1$ problem, during the second day — exactly $2$ problems, during the third day — exactly $3$ problems, and so on. During the $k$ -th day he should solve $k$ problems.

Polycarp has a list of $n$ contests, the $i$ -th contest consists of $a_i$ problems. During each day Polycarp has to choose exactly one of the contests he didn't solve yet and solve it. He solves exactly $k$ problems from this contest. Other problems are discarded from it. If there are no contests consisting of at least $k$ problems that Polycarp didn't solve yet during the $k$ -th day, then Polycarp stops his training.

How many days Polycarp can train if he chooses the contests optimally?

The first line of the input contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the number of contests.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 2 \cdot 10^5$ ) — the number of problems in the $i$ -th contest.

Print one integer — the maximum number of days Polycarp can train if he chooses the contests optimally.