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Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
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Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

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B. Polycarp Training

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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

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