Polycarp Training

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 ≤ n ≤ 2 ⋅ 10^5) — the number of contests.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 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

inputFormat

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of contests.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5) — the number of problems in the i-th contest.

outputFormat

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

样例

4
3 1 4 1

3

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