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.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;

public class A {

    void solve() throws IOException {
        int n = nI();
        int [] a = new int [n];
        int [] b = new int [n];
        int z = 0;
        int s = 0;
        for (int i = 0; i < n; i++) {
            a[i] = nI();
            z += a[i];
        }
        for (int i = 0; i < n; i++) {
            b[i] = nI();
            s += b[i];
        }
        s++;
        int [][]ar = new int [n+1][s];
        int [][]ar2 = new int [n+1][s];
        for (int i = 0; i < n+1; i++) {
            Arrays.fill(ar[i], -1);
        }
        ar[0][0] = 0;
        for (int i = 1; i < n+1; i++) {
            for (int j = 0; j < s; j++) {
                if (j==0) {
                    ar[i][j] = 0;
                }
                else if (j-b[i-1]>=0){
                    int qqq = ar[i-1][j-b[i-1]]+1;
                    int lll = ar[i-1][j];
                    if(qqq>0 && lll >=0 && qqq>lll){
                        ar[i][j] = lll;
                        ar2[i][j] = ar2[i - 1][j];
                    }else if(qqq>0 && lll >=0 && qqq<lll){
                        ar[i][j] = qqq;
                        ar2[i][j] = ar2[i-1][j-b[i-1]] + a[i-1];
                    }
                    else if(qqq>0 && lll >=0){
                        ar[i][j] = qqq;
                        ar2[i][j] = Math.max(ar2[i - 1][j],ar2[i-1][j-b[i-1]] + a[i-1]);
                    }
                    else if(qqq>0){
                        ar[i][j] = qqq;
                        ar2[i][j] = ar2[i-1][j-b[i-1]] + a[i-1];
                    }
                    else if(lll>=0){
                        ar[i][j] = lll;
                        ar2[i][j] = ar2[i - 1][j];
                    }
                }
                else {
                    if(ar[i-1][j]>=0){
                        ar[i][j] = ar[i-1][j];
                        ar2[i][j] = ar2[i-1][j];
                    }
                }

            }
        }
        int a1 = Integer.MAX_VALUE;
        int a2 = -1;
        for (int i = z; i < s; i++) {
            if (ar[n][i]>=0&&a1>ar[n][i]){
                a1 = ar[n][i];
                a2 = ar2[n][i];
            }
            else if(ar[n][i]>=0&&a1==ar[n][i]){
                a2 = Math.max(a2,ar2[n][i]);
            }
        }
        out.println(a1 + " " + (z-a2));
    }

    public static void main(String [] args) throws IOException {
        (new A()).run();
    }
    StreamTokenizer in;
    PrintWriter out;
    void run() throws IOException {
        in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        out = new PrintWriter(System.out);
        solve();
        out.flush();
        out.close();
    }
    int nI() throws IOException {
        in.nextToken();
        return (int)in.nval;
    }
    String nS() throws IOException {
        in.nextToken();
        return in.sval;
    }
}
