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.util.Arrays;
import java.util.StringTokenizer;

public class Bottles {
	static int[][][] dp;
	static int n;
	static int[] soda, cap;
	static Pair[] bottles;
	static int inf = (int) 10e7;
	
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		n = Integer.parseInt(br.readLine());
		StringTokenizer st = new StringTokenizer(br.readLine() + " " + br.readLine());
		soda = new int[n];
		cap = new int[n];
		bottles = new Pair[n];
		
		
		int total = 0;
		for (int i = 0; i < n; i++){
			soda[i] = Integer.parseInt(st.nextToken());
			total += soda[i];
		}
		
		for (int i = 0; i < n; i++) 
			cap[i] = Integer.parseInt(st.nextToken());
		
		for (int i = 0; i < n; i++) 
			bottles[i] = new Pair(cap[i], soda[i]);
		
		Arrays.sort(bottles);
		int k = 0;
		int max = total;
		
		for(int i = 0; i < n; i++) {
			if(max <= 0)
				break;
			max -= bottles[i].cap;
			k++;
		}
		
		dp = new int[n + 1][k + 1][100*100+1];
		for (int i = 0; i < dp.length; i++) 
			for (int j = 0; j < dp[i].length; j++) 
				for(int l = 0; l < dp[i][j].length; l++)
					dp[i][j][l] = -1;
		
		for(int[][] a: dp)
			for(int [] b : a)
				Arrays.fill(b, -1);
		
		int sol = solve(0, k, total);
//		System.out.println(sol);
		System.out.println(k + " " + (total - sol));
	}
	
	public static int solve(int i, int taken, int w)
	{
		if(taken == 0){
			if(w <= 0)
				return 0;
			else
				return -inf;
		}
		if(w <= 0)
			return 0;
		if(i >= n)
			return -inf;
		
		if(dp[i][taken][w] != -1)
			return dp[i][taken][w];
		
		int a = solve(i + 1, taken, w);
		int b = bottles[i].soda + solve(i + 1, taken - 1, w - bottles[i].cap);
		
		return dp[i][taken][w] = Math.max(a, b);
	}
	
	static class Pair implements Comparable<Pair>{
		int cap, soda;
		
		public Pair(int c, int s)
		{
			cap = c;
			soda = s;
		}

		@Override
		public int compareTo(Pair o) {
			return -((Integer)cap).compareTo(o.cap);
		}
		
		
	}
}