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.

// ~/BAU/ACM-ICPC/Teams/A++/BlackBurn95

import java.io.*;
import java.util.*;
import java.math.*;
import static java.lang.Math.*;
import static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.Double.parseDouble;
import static java.lang.String.*;

public class Main {

    static int n,offset = 20001,inf = (int)1e9;
    static int [] a,b;
    static pair [][] dp;
    
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                                              // (new FileReader("input.in"));
        StringBuilder out = new StringBuilder();
        StringTokenizer tk;
        
        n = parseInt(in.readLine());
        tk = new StringTokenizer(in.readLine());
        a = new int[n];
        for(int i=0; i<n; i++)
            a[i] = parseInt(tk.nextToken());
        tk = new StringTokenizer(in.readLine());
        b = new int[n];
        for(int i=0; i<n; i++)
            b[i] = parseInt(tk.nextToken());
        
        dp = new pair[n][10001+offset];
        
        pair ans = calc(0,0);
        
        System.out.println(ans.first+" "+ans.second);
    }

    static pair calc(int i,int val) {
        if(i==n) {
            if(val<=0) return new pair(0,val);
            return new pair(inf,inf);
        }
        
        if(dp[i][val+offset]!=null) {
            //System.out.println(val+" "+(val+offset));
            return dp[i][val+offset];
        }
        
        pair c1 = new pair(calc(i+1,val+a[i]));
        pair c2 = new pair(calc(i+1,val-(b[i]-a[i])));
        c2.first++;
        c2.second += max(b[i]-a[i],0*val);
        
        if(c1.first < c2.first) return dp[i][val+offset] = c1;
        if(c1.first > c2.first) return dp[i][val+offset] = c2;
        if(c1.second < c2.second) return dp[i][val+offset] = c1;
        return dp[i][val+offset] = c2;
    }
}

class pair {
    int first,second;
    
    public pair(int f,int s) {
        this.first = f;
        this.second = s;
    }
    
    public pair(pair c) {
        this.first = c.first;
        this.second = c.second;
    }
}
