You need to execute several tasks, each associated with number of processors it needs, and the compute power it will consume.

You have sufficient number of analog computers, each with enough processors for any task. Each computer can execute up to one task at a time, and no more than two tasks total. The first task can be any, the second task on each computer must use strictly less power than the first. You will assign between 1 and 2 tasks to each computer. You will then first execute the first task on each computer, wait for all of them to complete, and then execute the second task on each computer that has two tasks assigned.

If the average compute power per utilized processor (the sum of all consumed powers for all tasks presently running divided by the number of utilized processors) across all computers exceeds some unknown threshold during the execution of the first tasks, the entire system will blow up. There is no restriction on the second tasks execution. Find the lowest threshold for which it is possible.

Due to the specifics of the task, you need to print the answer multiplied by 1000 and rounded up.

Input

The first line contains a single integer n (1 ≤ n ≤ 50) — the number of tasks.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 108), where ai represents the amount of power required for the i-th task.

The third line contains n integers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the number of processors that i-th task will utilize.

Output

Print a single integer value — the lowest threshold for which it is possible to assign all tasks in such a way that the system will not blow up after the first round of computation, multiplied by 1000 and rounded up.

Examples

Input

6
8 10 9 9 8 10
1 1 1 1 1 1


Output

9000


Input

6
8 10 9 9 8 10
1 10 5 5 1 10


Output

1160

Note

In the first example the best strategy is to run each task on a separate computer, getting average compute per processor during the first round equal to 9.

In the second task it is best to run tasks with compute 10 and 9 on one computer, tasks with compute 10 and 8 on another, and tasks with compute 9 and 8 on the last, averaging (10 + 10 + 9) / (10 + 10 + 5) = 1.16 compute power per processor during the first round.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DComputePower solver = new DComputePower();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DComputePower {
        Debug debug = new Debug(true);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            Task[] tasks = new Task[n + 1];
            for (int i = 1; i <= n; i++) {
                tasks[i] = new Task();
                tasks[i].a = in.readInt();
            }

            int bSum = 0;
            for (int i = 1; i <= n; i++) {
                tasks[i].b = in.readInt();
                bSum += tasks[i].b;
            }

            Arrays.sort(tasks, 1, n + 1, (a, b) -> a.a == b.a ? -Long.compare(a.b, b.b) : -Long.compare(a.a, b.a));
            long[][][] dp = new long[n + 1][n + 1][bSum + 1];
            long inf = (long) 1e15;
            SequenceUtils.deepFill(dp, (long) inf);
            dp[0][0][0] = 0;
            for (int i = 1; i <= n; i++) {
                int r = i;
                while (r + 1 <= n && tasks[r + 1].a == tasks[i].a) {
                    r++;
                }
                int m = r - i + 1;
                long[] prefixA = new long[m + 1];
                int[] prefixB = new int[m + 1];
                for (int j = 0; j < m; j++) {
                    prefixA[j + 1] = tasks[i + j].a;
                    prefixB[j + 1] = tasks[i + j].b;
                }
                LongPreSum aPs = new LongPreSum(prefixA);
                IntegerPreSum bPs = new IntegerPreSum(prefixB);

                for (int t = 0; t <= m; t++) {
                    int frontCnt = t;
                    int backCnt = m - t;
                    long frontA = aPs.prefix(t);
                    int frontB = bPs.prefix(t);

                    for (int j = 0; j <= n; j++) {
                        for (int k = 0; k <= bSum; k++) {
                            // add as first
                            if (j >= backCnt && j - backCnt + frontCnt <= n && k + frontB <= bSum) {
                                dp[r][j - backCnt + frontCnt][k + frontB] = Math.min(dp[r][j - backCnt + frontCnt][k + frontB], dp[i - 1][j][k] + frontA);
                            }
                        }
                    }
                }
            }


            debug.debug("dp", dp);
            long min = inf;
            for (int i = 0; i <= n; i++) {
                for (int j = 1; j <= bSum; j++) {
                    min = Math.min(min, DigitUtils.ceilDiv(dp[n][i][j] * 1000, j));
                }
            }

            out.println(min);
        }

    }

    static class LongPreSum {
        private long[] pre;
        private int n;

        public LongPreSum(int n) {
            pre = new long[n];
        }

        public void populate(long[] a) {
            n = a.length;
            pre[0] = a[0];
            for (int i = 1; i < n; i++) {
                pre[i] = pre[i - 1] + a[i];
            }
        }

        public LongPreSum(long[] a) {
            this(a.length);
            populate(a);
        }

        public long prefix(int i) {
            if (i < 0) {
                return 0;
            }
            return pre[Math.min(i, n - 1)];
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, long val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof long[]) {
                long[] longArray = (long[]) array;
                Arrays.fill(longArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

    }

    static class IntegerPreSum {
        private int[] pre;
        private int n;

        public IntegerPreSum(int n) {
            pre = new int[n];
        }

        public void populate(int[] a) {
            n = a.length;
            pre[0] = a[0];
            for (int i = 1; i < n; i++) {
                pre[i] = pre[i - 1] + a[i];
            }
        }

        public IntegerPreSum(int[] a) {
            this(a.length);
            populate(a);
        }

        public int prefix(int i) {
            if (i < 0) {
                return 0;
            }
            return pre[Math.min(i, n - 1)];
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static long floorDiv(long a, long b) {
            return a < 0 ? -ceilDiv(-a, b) : a / b;
        }

        public static long ceilDiv(long a, long b) {
            if (a < 0) {
                return -floorDiv(-a, b);
            }
            long c = a / b;
            if (c * b < a) {
                return c + 1;
            }
            return c;
        }

    }

    static class Task {
        long a;
        int b;

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }
}

