Problem:
Score : 300 points

Problem Statement

In AtCoder, a person who has participated in a contest receives a color, which corresponds to the person's rating as follows:

Rating 1-399 : gray

Rating 400-799 : brown

Rating 800-1199 : green

Rating 1200-1599 : cyan

Rating 1600-1999 : blue

Rating 2000-2399 : yellow

Rating 2400-2799 : orange

Rating 2800-3199 : red

Other than the above, a person whose rating is 3200 or higher can freely pick his/her color, which can be one of the eight colors above or not.

Currently, there are N users who have participated in a contest in AtCoder, and the i-th user has a rating of a_i.

Find the minimum and maximum possible numbers of different colors of the users.

Constraints

1 ≤ N ≤ 100

1 ≤ a_i ≤ 4800

a_i is an integer.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum possible number of different colors of the users, and the maximum possible number of different colors, with a space in between.

Sample Input 1

4
2100 2500 2700 2700

Sample Output 1

2 2

The user with rating 2100 is "yellow", and the others are "orange". There are two different colors.

Sample Input 2

5
1100 1900 2800 3200 3200

Sample Output 2

3 5

The user with rating 1100 is "green", the user with rating 1900 is blue and the user with rating 2800 is "red".

If the fourth user picks "red", and the fifth user picks "blue", there are three different colors. This is one possible scenario for the minimum number of colors.

If the fourth user picks "purple", and the fifth user picks "black", there are five different colors. This is one possible scenario for the maximum number of colors.

Sample Input 3

20
800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990

Sample Output 3

1 1

All the users are "green", and thus there is one color.

Solution in Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int dataCount = sc.nextInt();

        // レート表
        LeaderBoard board = new LeaderBoard();

        for (int i = 0; i < dataCount; i++) {
            board.addRate(sc.nextInt());
        }

        System.out.println(board.getMinPattern() + " " + board.getMaxPattern());
    }
}

class Rate {
    private Integer min;
    private Integer max;
    private boolean freeColor;

    public Rate(Integer min, Integer max, boolean freeColor) {
        this.min = min;
        this.max = max;
        this.freeColor = freeColor;
    }

    public boolean isInRange(int rate) {
        if (this.max != null) {
            if (this.min <= rate && this.max >= rate) {
                return true;
            } else {
                return false;
            }
        } else {
            if (this.min <= rate) {
                return true;
            } else {
                return false;
            }
        }
    }

    @Override
    public int hashCode() {
        final int prime = 31;
        int result = 1;
        result = prime * result + (freeColor ? 1231 : 1237);
        result = prime * result + ((max == null) ? 0 : max.hashCode());
        result = prime * result + ((min == null) ? 0 : min.hashCode());
        return result;
    }

    @Override
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Rate other = (Rate) obj;
        if (freeColor != other.freeColor)
            return false;
        if (max == null) {
            if (other.max != null)
                return false;
        } else if (!max.equals(other.max))
            return false;
        if (min == null) {
            if (other.min != null)
                return false;
        } else if (!min.equals(other.min))
            return false;
        return true;
    }

    public Integer getMin() {
        return min;
    }

    public void setMin(Integer min) {
        this.min = min;
    }

    public Integer getMax() {
        return max;
    }

    public void setMax(Integer max) {
        this.max = max;
    }

    public boolean isFreeColor() {
        return freeColor;
    }

    public void setFreeColor(boolean freeColor) {
        this.freeColor = freeColor;
    }
}

class LeaderBoard {
    private Map<Rate, Integer> rateDispersion;

    public LeaderBoard() {
        rateDispersion = new HashMap<>();

        // 初期データ生成
        rateDispersion.put(createRate(1, 399, false), 0);
        rateDispersion.put(createRate(400, 799, false), 0);
        rateDispersion.put(createRate(800, 1199, false), 0);
        rateDispersion.put(createRate(1200, 1599, false), 0);
        rateDispersion.put(createRate(1600, 1999, false), 0);
        rateDispersion.put(createRate(2000, 2399, false), 0);
        rateDispersion.put(createRate(2400, 2799, false), 0);
        rateDispersion.put(createRate(2800, 3199, false), 0);
        rateDispersion.put(createRate(3200, null, true), 0);
    }

    public void addRate(int rate) {

        // 指定範囲内のrateに人数を加算
        for (Rate key : rateDispersion.keySet()) {
            if (key.isInRange(rate)) {
                rateDispersion.put(key, rateDispersion.get(key) + 1);

                return;
            }
        }
    }

    public int getMaxPattern() {
        int patterns = 0;

        for (Map.Entry<Rate, Integer> entry : rateDispersion.entrySet()) {
            if (!entry.getKey().isFreeColor() && entry.getValue() != null && entry.getValue() > 0) {
                patterns += 1;
            }
        }

        // 色自由分の計算
        List<Rate> freeColorList = new ArrayList<>();

        for (Map.Entry<Rate, Integer> entry : rateDispersion.entrySet()) {
            if (entry.getKey().isFreeColor()) {
                freeColorList.add(entry.getKey());
            }
        }

        for (Rate freeColorRate : freeColorList) {
            Integer count = rateDispersion.get(freeColorRate);

            for (int i = 0; i < count; i++) {
                patterns += 1;
            }
        }

        return patterns;
    }

    public int getMinPattern() {
        int patterns = 0;
        boolean foundFreeColor = false;

        // 色自由をカウントしなければ最小値
        for (Map.Entry<Rate, Integer> entry : rateDispersion.entrySet()) {
            if (!entry.getKey().isFreeColor() && entry.getValue() != null && entry.getValue() > 0) {
                patterns += 1;
            }

            if (!foundFreeColor && entry.getKey().isFreeColor() && entry.getValue() != null && entry.getValue() > 0) {
                foundFreeColor = true;
            }
        }

        if (foundFreeColor && patterns == 0) {
            patterns = 1;
        }

        return patterns;
    }

    private Rate createRate(Integer min, Integer max, boolean freeColor) {
        return new Rate(min, max, freeColor);
    }

}