Maximum Days of Problem Solving

Problem Description

Xiao Yang made a problem-solving plan to improve himself: on day $k$, he must solve $k$ problems, otherwise he will slack off.

Xiao Yang found a problem bank consisting of $n$ problem sets, each containing some number of problems. He is very picky: he will use each problem set at most once, and on any given day he can only use problems from a single problem set, after which that set is discarded and cannot be used again. For each problem set, he does not have to finish all the problems in it.

The question is: what is the maximum number of consecutive days Xiao Yang can keep up his plan before he has to slack off?

Input Format

The first line contains an integer $n$, the number of problem sets.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$, the number of problems in each problem set.

Output Format

Output one line containing a single integer: the answer.

Sample Input

4
3 1 4 1

Sample Output

3

Sample Explanation

There are $4$ problem sets with $3, 1, 4, 1$ problems respectively.

• On day $1$, he needs to solve $1$ problem; he can pick the set with $1$ problem.
• On day $2$, he needs to solve $2$ problems; he can pick the set with $3$ problems (solving only $2$ of them).
• On day $3$, he needs to solve $3$ problems; he can pick the set with $4$ problems (solving only $3$ of them).

By day $4$ he would need to solve $4$ problems, but the remaining set only has $1$ problem, which is insufficient, so he can keep going for at most $3$ days.

Constraints

For all test data, $1 \le n \le 10^6$ and $1 \le a_i \le 10^9$ are guaranteed.