Polycarp Training
Description
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.
Input
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.
Output
Print one integer — the maximum number of days Polycarp can train if he chooses the contests optimally.
Samples
4
3 1 4 1
3
3
1 1 1
1
5
1 1 1 2 2
2