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.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static long mod = 17352642619633L;

    void run(FastScanner in, PrintWriter out) {

        // dp[i][overflow]

        int N = in.nextInt();
        int[] a = new int[N];
        int[] b = new int[N];

        int[][] dp = new int[N+1][20_002];
        int[][] dpTime = new int[N+1][20_002];
        for (int[] d : dp) Arrays.fill(d, Integer.MAX_VALUE);
        for (int[] d : dpTime) Arrays.fill(d, Integer.MAX_VALUE);
        int d = 10_000;
        dp[0][d] = 0;
        dpTime[0][d] = 0;

        for (int i = 0; i < N; i++) a[i] = in.nextInt();
        for (int i = 0; i < N; i++) b[i] = in.nextInt();

        for (int i = 0; i < N; i++) {

            for (int overflow = 0; overflow < dp[0].length; overflow++) {
                if (dp[i][overflow] == Integer.MAX_VALUE) continue;

                // sink
                if (dp[i][overflow] + 1 < dp[i+1][overflow-(b[i]-a[i])]) {
                    dp[i+1][overflow-(b[i]-a[i])] = dp[i][overflow] + 1;
                    dpTime[i+1][overflow-(b[i]-a[i])] = dpTime[i][overflow];
                } else if (dp[i][overflow] + 1 == dp[i+1][overflow-(b[i]-a[i])]) {
                    dpTime[i+1][overflow-(b[i]-a[i])] =
                        Math.min(dpTime[i+1][overflow-(b[i]-a[i])], dpTime[i][overflow]);
                }

                // source
                if (dp[i][overflow] < dp[i+1][overflow+a[i]]) {
                    dp[i+1][overflow+a[i]] = dp[i][overflow];
                    dpTime[i+1][overflow+a[i]] = dpTime[i][overflow] + a[i];

                } else if (dp[i][overflow] == dp[i+1][overflow+a[i]]) {
                    dpTime[i+1][overflow+a[i]] =
                        Math.min(dpTime[i+1][overflow+a[i]], dpTime[i][overflow]+a[i]);
                }

            }
        }

        int min = Integer.MAX_VALUE;
        int minTime = Integer.MAX_VALUE;
        for (int i = d; i >= 0; i--) {
            if (dp[N][i] < min) {
                min = dp[N][i];
                minTime = dpTime[N][i];
            } else if (dp[N][i] == min) {
                minTime = Math.min(minTime, dpTime[N][i]);
            }
        }

        out.println(min + " " + minTime);

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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