Q-index

Interview

Time limit1sMemory limit512 MB

Summary

Given n citation counts, find the largest k such that at least k papers have k or more citations and the rest have at most k.

Level: Medium4 of 10
Topics: Sorting, Array
Solved: No attempts yet

Problem

ICPC University sets its doctoral graduation requirement from the number of papers a student has published and how often those papers are cited, and it measures this with a value called the q-index. Suppose a student has published $n$ papers, where $n \ge 1$ . The student's q-index is $k$ when at least $k$ papers are cited $k$ or more times and each of the remaining $n - k$ papers is cited at most $k$ times.

Take a student with 5 papers cited 8, 4, 5, 3, and 10 times. At least one paper is cited one or more times, but some of the other 4 papers are cited more than once, so the q-index is not 1. Fewer than 5 papers are cited 5 or more times, so it is not 5 either. Exactly 4 papers are cited 4 or more times and the one remaining paper is cited at most 4 times, so this student's q-index is 4.

Write a program that reads the citation counts of one student's papers and computes that student's q-index.

Input

The first line contains the number of papers $n$ the student published, where $1 \le n \le 1000$ . The second line contains the citation counts of the $n$ papers in order, separated by spaces. Each citation count is an integer between 0 and 10000.

Output

Print the q-index on one line. The value is a non-negative integer.

Examples3

Example 1
Input
```
5
8 4 5 3 10
```
Expected output
```
4
```
Example 2
Input
```
4
0 0 0 0
```
Expected output
```
0
```
Example 3
Input
```
6
12 7 6 8 9 10
```
Expected output
```
6
```