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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;


public class J {

	static StringTokenizer st;
	static BufferedReader br;
	static PrintWriter pw;
	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = nextInt();
		int[]a = new int[n+1], b = new int[n+1];
		int s1 = 0, s2 = 0;
		for (int i = 1; i <= n; i++) {
			a[i] = nextInt();
			s1 += a[i];
		}
		ArrayList<Integer>L = new ArrayList<Integer>();
		for (int i = 1; i <= n; i++) {
			b[i] = nextInt();
			s2 += b[i];
			L.add(b[i]);
		}
		Collections.sort(L);
		int sum = 0, k = 0;
		for (int i = L.size()-1; i >= 0; i--) {
			sum += L.get(i);
			k++;
			if (sum >= s1) {
				break;
			}
		}
		int s = s2-s1+1;
		k = n - k;
		int[][]dp = new int[s+1][k+1];
		int INF = (int) 1e9;
		for (int i = 0; i <= s; i++) {
			for (int j = 0; j <= k; j++) {
				dp[i][j] = INF;
			}
		}
		dp[0][0] = 0;
		for (int i = 1; i <= n; i++) {
			for (int j = s; j >= 0; j--) {
				for (int j2 = 0; j2 <= k; j2++) {
					if (j >= b[i] && j2 > 0) {
						dp[j][j2] = Math.min(dp[j][j2], dp[j-b[i]][j2-1] + a[i]);
					}
				}
			}
		}
		int t = INF;
		for (int i = 0; i <= s2-s1; i++) {
			t = Math.min(t, dp[i][k]);
		}
		k = n-k;
		System.out.println(k+" "+t);
		pw.close();
	}
	private static int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	private static long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	private static double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	private static String next() throws IOException {
		while (st==null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}
}