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 Bottles {

	static class Bottle {
		int a, b;

		Bottle(int x, int y) {
			a = x;
			b = y;
		}

		@Override
		public String toString() {
			return a + " " + b;
		}
	}

	static final int oo = 1 << 28;
	static final int MAX = 10001;

	static int N;
	static Bottle[] b;
	static int[][][] dp;

	static int solve(int k, int idx, int volume) {
		if(k == 0)
			return volume <= 0 ? 0 : -oo;
		if(idx == N)
			return -oo;
		if (dp[k][idx][volume] != -1)
			return dp[k][idx][volume];
		return dp[k][idx][volume] = Math.max(solve(k - 1, idx + 1, volume - b[idx].b) + b[idx].a,
				solve(k, idx + 1, volume));
	}

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		N = sc.nextInt();
		int need = 0;
		int[] a = new int[N];
		for (int i = 0; i < N; i++)
			need += a[i] = sc.nextInt();
		b = new Bottle[N];
		for (int i = 0; i < N; i++)
			b[i] = new Bottle(a[i], sc.nextInt());
		Arrays.sort(b, (x, y) -> x.b - y.b);
		int volume = 0, numBottles;
		for (numBottles = N - 1; numBottles >= 0 && volume < need; numBottles--)
			volume += b[numBottles].b;
		numBottles = N - numBottles - 1;
		dp = new int[numBottles + 1][N][need + 1];
		for (int i = 0; i <= numBottles; i++)
			for (int j = 0; j < N; j++)
				Arrays.fill(dp[i][j], -1);
		out.printf("%d %d\n", numBottles, need - solve(numBottles, 0, need));
		out.flush();
		out.close();
	}

	static class MyScanner {

		BufferedReader br;
		StringTokenizer st;

		MyScanner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

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

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

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

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