Game "Drunkard"

Input

The first line contains a single integer $n$ (1 \le n \le 10^5), representing the number of cards each player holds.

The second line lists $n$ distinct integers a_1, a_2, \dots, a_n (1 \le a_i \le 2n), which are the values of Vitalii's cards.

Output

Output two integers: the minimum and maximum number of points Vitalii can score.

Examples

Note

Consider the first example where Vitalii's cards are $1,4,5$, and Bohdan's cards are $2,3,6$. Here are two possible outcomes:

1. Vitalii plays $1$, Bohdan plays $6$. Bohdan scores because 1 < 6.

2. Vitalii plays $4$, Bohdan plays $2$. Vitalii scores because 4 > 2.

3. Vitalii plays $5$, Bohdan plays $3$. Vitalii scores because 5 > 3.

Vitalii scores two points.

In another scenario:

1. Vitalii plays $1$, Bohdan plays $2$. Bohdan scores because 1 < 2.

2. Vitalii plays $4$, Bohdan plays $6$. Bohdan scores because 4 < 6.

3. Vitalii plays $5$, Bohdan plays $3$. Vitalii scores because 5 > 3.

Vitalii scores one point.

By examining all possible outcomes, it is evident that Vitalii cannot score fewer than one point or more than two points.

In the second example, Vitalii's cards are $4,5,6$, and Bohdan's cards are $1,2,3$. Here, every card Vitalii plays is greater than any card Bohdan plays, so Vitalii scores exactly $3$ points in every scenario.

Scoring

Solutions that correctly handle the constraints 1 \le n \le 2\,000 will earn $40\%$ of the total points.