Nick has n bottles of soda left after his birthday. Each bottle is described by two values: remaining amount of soda ai and bottle volume bi (ai ≤ bi).

Nick has decided to pour all remaining soda into minimal number of bottles, moreover he has to do it as soon as possible. Nick spends x seconds to pour x units of soda from one bottle to another.

Nick asks you to help him to determine k — the minimal number of bottles to store all remaining soda and t — the minimal time to pour soda into k bottles. A bottle can't store more soda than its volume. All remaining soda should be saved.

Input

The first line contains positive integer n (1 ≤ n ≤ 100) — the number of bottles.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 100), where ai is the amount of soda remaining in the i-th bottle.

The third line contains n positive integers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the volume of the i-th bottle.

It is guaranteed that ai ≤ bi for any i.

Output

The only line should contain two integers k and t, where k is the minimal number of bottles that can store all the soda and t is the minimal time to pour the soda into k bottles.

Examples

Input

4
3 3 4 3
4 7 6 5


Output

2 6


Input

2
1 1
100 100


Output

1 1


Input

5
10 30 5 6 24
10 41 7 8 24


Output

3 11

Note

In the first example Nick can pour soda from the first bottle to the second bottle. It will take 3 seconds. After it the second bottle will contain 3 + 3 = 6 units of soda. Then he can pour soda from the fourth bottle to the second bottle and to the third bottle: one unit to the second and two units to the third. It will take 1 + 2 = 3 seconds. So, all the soda will be in two bottles and he will spend 3 + 3 = 6 seconds to do it.
import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws IOException {


        new Main().solve();
    }

    int mod = 1000000007;

    //15084000000000

    PrintWriter out;

    int n;

    void solve() throws IOException {

        Reader in;

        try {

            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }

        //BufferedReader br = new BufferedReader( new FileReader("in.txt") );
        //BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );

        int n = in.nextInt();

        int[] d1 = new int[10010];
        int[] d2 = new int[10010];

        int[] a = new int[n];
        int[] b = new int[n];

        int sum = 0;
        for (int i = 0; i < n; i++) {

            a[i] = in.nextInt();
            sum += a[i];
        }

        for (int i = 0; i < n; i++) {

            b[i] = in.nextInt();
        }

        Arrays.fill(d1, 1000000000);
        d1[0] = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 10000; j >= 0; j--)
                if (j+b[i] <= 10000) {

                    if (d1[j]+1 < d1[j+b[i]]) {
                        d1[j+b[i]] = d1[j]+1;
                        d2[j+b[i]] = d2[j]+a[i];
                    }
                    else
                    if (d1[j]+1 == d1[j+b[i]] && d2[j+b[i]] < d2[j]+a[i])
                    {
                        d2[j+b[i]] = d2[j]+a[i];
                    }
                }
        }

        int k = 10000;
        int min = 0;

        for (int i = sum; i <= 10000; i++) {

            if (d1[i] < k) {
                k = d1[i];
                min = d2[i];
            }
            else
            if (d1[i] == k && min < d2[i]) {
                min = d2[i];
            }
        }

        out.println(k+" "+(sum-min));
        out.flush();
        out.close();
    }

    class Pair implements Comparable<Pair>{

        long a;
        long b;


        Pair(long a, long b) {

            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair p) {

            if (a < p.a)
                return -1;

            if (a > p.a)
                return 1;

            if  (b < p.b)
                return -1;

            if (b > p.b)
                return 1;

            return 0;
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }

    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

    }

}