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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.Arrays;


public class Main {
    static StreamTokenizer in=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));  
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));  
      
    public static int nextInt()throws IOException {in.nextToken();return (int)in.nval;}  
    public static long nextLong()throws IOException {in.nextToken(); return (long)in.nval;}
    public static String next()throws IOException {in.nextToken();return (String)in.sval;}  

    static  int[] a = new int[120], b = new int[120];

    
    public static void main(String[] args) throws IOException {
    	int n = nextInt();
    	int sum = 0;
    	for (int i = 1; i <= n; i++) {
    		a[i] = nextInt();
    		sum += a[i];
    	}
    	for (int i = 1; i <= n; i++)
    		b[i] = nextInt();
    	qsort(1, n);
    	int k = 0;
    	for (int i = 1; i <= n; i++) {
    		k += b[i];
    		if (k >= sum) {
    			k = i;
    			break;
    		}
    	}
    	int[][] f = new int[105][100100];
    	for (int i = 0; i < 105; i++)
    		Arrays.fill(f[i], -1);
    	f[0][0] = 0;
    	for (int i = 1; i <= n; i++)
    		for (int j = sum - a[i]; j >= 0; j--)
    			for (int pre = i - 1; pre >= 0; pre--)
    				if (f[pre][j] != -1) 
    					f[pre + 1][j + a[i]] = Math.max(f[pre + 1][j + a[i]], f[pre][j] + b[i]);
    	int t = 0;
    	for (int i = sum; i >= 0; i--)
    		if (f[k][i] >= sum) {
    			t = i;
    			break;
    		}
    	out.println(k + " " + (sum - t));
    	out.flush();
    	out.close();
    }
    public static void qsort(int head, int tail) {
    	int x = b[(head + tail) / 2];
    	int i = head, j = tail;
    	while(i < j) {
    		while (b[i] > x) i++;
    		while (b[j] < x) j--;
    		if (i <= j) {
    			int k = b[i];
    			b[i] = b[j];
    			b[j] = k;
    			k = a[i];
    			a[i] = a[j];
    			a[j] = k;
    			i++;
    			j--;
    		}
    	}
    	if (head < j) qsort(head, j);
    	if (i < tail) qsort(i, tail);
    }
}

  	    		 	 						  		 	 			