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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class A {

	static final int INF = (int)1e9;
	
	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int n = sc.nextInt();
		Bottle[] bots = new Bottle[n];
		int soda = 0;
		for(int i = 0; i < n; ++i)
		{
			bots[i] = new Bottle(sc.nextInt());
			soda += bots[i].a;
		}
		for(int i = 0; i < n; ++i)
			bots[i].b = sc.nextInt();
		Arrays.sort(bots);
		int k = 0, vol = 0;
		while(vol < soda)
			vol += bots[k++].b;
		int[][][] dp = new int[n + 1][k + 1][soda + 1];
		for(int[] x: dp[n])
			Arrays.fill(x, INF);
		dp[n][0][0] = 0;
		for(int idx = n - 1; idx >= 0; --idx)
			for(int remK = 0; remK <= k; ++remK)
				for(int curSoda = 0; curSoda <= soda; ++curSoda)
				{
					int ret = dp[idx + 1][remK][curSoda] + bots[idx].a;
					if(remK > 0)
						ret = Math.min(ret, dp[idx + 1][remK - 1][Math.max(curSoda - bots[idx].b, 0)]);
					dp[idx][remK][curSoda] = ret;
				}		
		out.println(k + " " + dp[0][k][soda]);
		out.flush();
		out.close();
	}
	
	static class Bottle implements Comparable<Bottle>
	{
		int a, b;
		
		Bottle(int x) { a = x; }
		
		public int compareTo(Bottle x) { return x.b - b; }
	}

	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}

		public long nextLong() throws IOException {return Long.parseLong(next());}

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

		public double nextDouble() throws IOException { return Double.parseDouble(next()); }

		public boolean ready() throws IOException {return br.ready();} 
	}
} 