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.*;
import java.util.*;

public class J {
    public static void solution(BufferedReader reader, PrintWriter writer)
            throws IOException {
        In in = new In(reader);
        Out out = new Out(writer);
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);
        int[] b = in.nextIntArray(n);
        int total = 0;
        for (int i = 0; i < n; i++)
            total += a[i];
        int MAX = 10000;
        int[][][] dp = new int[n + 1][n + 1][MAX + 1];
        for (int i = 0; i <= n; i++)
            for (int j = 0; j <= n; j++)
                Arrays.fill(dp[i][j], -1);
        dp[0][0][0] = 0;
        for (int i = 0; i < n; i++)
            for (int j = 0; j <= i; j++)
                for (int k = 0; k <= MAX; k++)
                    if (dp[i][j][k] != -1) {
                        dp[i + 1][j][k] = Math.max(dp[i + 1][j][k],
                                dp[i][j][k]);
                        dp[i + 1][j + 1][k + b[i]] = Math.max(
                                dp[i + 1][j + 1][k + b[i]], dp[i][j][k] + a[i]);
                    }
        int k = n, t = MAX;
        for (int i = 0; i <= k; i++)
            for (int j = total; j <= MAX; j++)
                if (dp[n][i][j] != -1) {
                    k = i;
                    t = Math.min(t, total - dp[n][i][j]);
                }
        out.println(String.format("%d %d", k, t));
    }

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(
                new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(System.out)));
        solution(reader, writer);
        writer.close();
    }

    protected static class In {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public In(BufferedReader reader) {
            this.reader = reader;
        }

        public String next() throws IOException {
            while (!tokenizer.hasMoreTokens())
                tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }

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

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

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

        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public int[] nextIntArray1(int n) throws IOException {
            int[] a = new int[n + 1];
            for (int i = 1; i <= n; i++)
                a[i] = nextInt();
            return a;
        }

        public int[] nextIntArraySorted(int n) throws IOException {
            int[] a = nextIntArray(n);
            Random r = new Random();
            for (int i = 0; i < n; i++) {
                int j = i + r.nextInt(n - i);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
            Arrays.sort(a);
            return a;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        public long[] nextLongArray1(int n) throws IOException {
            long[] a = new long[n + 1];
            for (int i = 1; i <= n; i++)
                a[i] = nextLong();
            return a;
        }

        public long[] nextLongArraySorted(int n) throws IOException {
            long[] a = nextLongArray(n);
            Random r = new Random();
            for (int i = 0; i < n; i++) {
                int j = i + r.nextInt(n - i);
                long t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
            Arrays.sort(a);
            return a;
        }
    }

    protected static class Out {
        private PrintWriter writer;
        private static boolean local = System
                .getProperty("ONLINE_JUDGE") == null;

        public Out(PrintWriter writer) {
            this.writer = writer;
        }

        public void print(char c) {
            writer.print(c);
        }

        public void print(int a) {
            writer.print(a);
        }

        public void println(String s) {
            writer.println(s);
        }

        public void println(int a) {
            writer.println(a);
        }

        public void println(long a) {
            writer.println(a);
        }

        public void println(Object[] os) {
            for (int i = 0; i < os.length; i++) {
                writer.print(os[i]);
                writer.print(' ');
            }
            writer.println();
        }

        public void println(int[] a) {
            for (int i = 0; i < a.length; i++) {
                writer.print(a[i]);
                writer.print(' ');
            }
            writer.println();
        }

        public void println(long[] a) {
            for (int i = 0; i < a.length; i++) {
                writer.print(a[i]);
                writer.print(' ');
            }
            writer.println();
        }

        public static void db(Object... objects) {
            if (local)
                System.out.println(Arrays.deepToString(objects));
        }
    }
}
