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B. Polycarp Training
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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?

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.

Examples
Input
4
3 1 4 1
Output
3
Input
3
1 1 1
Output
1
Input
5
1 1 1 2 2
Output
2