## a-index

David has been developing apps. To show off the productivity and impact of David's development, David has come up with a metric which David is calling an a-index.

As David is busy developing the next big app, David has gotten you to write a program to calculate an a-index.

An a-index is calculated as the largest integer \(a\) such that the developer has developed \(a\) applications that each have at least \(a\) users.

Given the number of users on each app that a developer has written, what is the developer's a-index?

#### Input Specification

The first line contains one integer, \(n (1 \leq n \leq 10^{5})\), the number of applications that a developer has developed.

The next line contains \(n\) space separated integers \(u_i (0 \leq u_i \leq 10^{9})\), the number of users for the \(i^{th}\) app.

#### Output Specification

A single integer \(a\), the developer's a-index.

#### Sample Input 1

```
1
0
```

#### Sample Output 1

`0`

#### Sample Input 2

```
1
1
```

#### Sample Output 2

`1`

#### Sample Input 3

```
3
3 2 3
```

#### Sample Output 3

`2`

#### Sample Input 4

```
4
9 1 1 1
```

#### Sample Output 4

`1`

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