Problem: Mikhail the Freelancer dreams of two things: to become a cool programmer and to buy a flat in Moscow. To become a cool programmer, he needs at least p experience points, and a desired flat in Moscow costs q dollars. Mikhail is determined to follow his dreams and registered at a freelance site.

He has suggestions to work on n distinct projects. Mikhail has already evaluated that the participation in the i-th project will increase his experience by ai per day and bring bi dollars per day. As freelance work implies flexible working hours, Mikhail is free to stop working on one project at any time and start working on another project. Doing so, he receives the respective share of experience and money. Mikhail is only trying to become a cool programmer, so he is able to work only on one project at any moment of time.

Find the real value, equal to the minimum number of days Mikhail needs to make his dream come true.

For example, suppose Mikhail is suggested to work on three projects and a1 = 6, b1 = 2, a2 = 1, b2 = 3, a3 = 2, b3 = 6. Also, p = 20 and q = 20. In order to achieve his aims Mikhail has to work for 2.5 days on both first and third projects. Indeed, a1·2.5 + a2·0 + a3·2.5 = 6·2.5 + 1·0 + 2·2.5 = 20 and b1·2.5 + b2·0 + b3·2.5 = 2·2.5 + 3·0 + 6·2.5 = 20.

Input

The first line of the input contains three integers n, p and q (1 ≤ n ≤ 100 000, 1 ≤ p, q ≤ 1 000 000) — the number of projects and the required number of experience and money.

Each of the next n lines contains two integers ai and bi (1 ≤ ai, bi ≤ 1 000 000) — the daily increase in experience and daily income for working on the i-th project.

Output

Print a real value — the minimum number of days Mikhail needs to get the required amount of experience and money. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6. 

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if <image>.

Examples

Input

3 20 20
6 2
1 3
2 6


Output

5.000000000000000


Input

4 1 1
2 3
3 2
2 3
3 2


Output

0.400000000000000

Note

First sample corresponds to the example in the problem statement.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() {
        return Long.parseLong(readString());
    }

    double readDouble() {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    class Point implements Comparable<Point> {
        long x;
        long y;

        public Point(long x, long y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public int compareTo(Point o) {
            int cmp = Long.compare(x, o.x);
            if (cmp == 0) {
                cmp = Long.compare(y, o.y);
            }
            return cmp;
        }
    }

    long obliquity(Point a, Point b, Point c) {
        long abx = b.x - a.x;
        long aby = b.y - a.y;

        long acx = c.x - a.x;
        long acy = c.y - a.y;
        return abx * acy - aby * acx;
    }

    boolean cw(Point a, Point b, Point c) {
        return obliquity(a, b, c) < 0;
    }

    boolean ccw(Point a, Point b, Point c) {
        return obliquity(a, b, c) > 0;
    }

    List<Point> convex(Point[] pts) {
        Arrays.sort(pts);
        List<Point> up = new ArrayList<>();
        List<Point> down = new ArrayList<>();

        Point p1 = pts[0];
        Point p2 = pts[pts.length - 1];
        up.add(p1);
        down.add(p1);

        for (int i = 1; i < pts.length; i++) {
            if (i == pts.length - 1 || cw(p1, pts[i], p2)) {
                while (up.size() >= 2 && !cw(up.get(up.size() - 2), up.get(up.size() - 1), pts[i])) {
                    up.remove(up.size() - 1);
                }
                up.add(pts[i]);
            }

            if (i == pts.length - 1 || ccw(p1, pts[i], p2)) {
                while (down.size() >= 2 && !ccw(down.get(down.size() - 2), down.get(down.size() - 1), pts[i])) {
                    down.remove(down.size() - 1);
                }
                down.add(pts[i]);
            }
        }
        List<Point> convex = new ArrayList<>();
        convex.addAll(up);
        for (int i = down.size() - 2; i > 0; i--) {
            convex.add(down.get(i));
        }
        return convex;
    }


    double time(Point p) {
        return Math.max(1d * P / p.x, 1d * Q / p.y);
    }

    double time(Point a, Point b) {
        double l = 0;
        double r = 1;

        if (!intersect(a.x, a.y, b.x, b.y, PF, QF)) {
            return Double.MAX_VALUE;
        }

        for (int i = 0; i < 70; i++) {
            double mid = (l + r) / 2;

            double dp = PF * mid;
            double dq = QF * mid;

            if (intersect(a.x, a.y, b.x, b.y, dp, dq)) {
                r = mid;
            } else {
                l = mid;
            }
        }

        double dp = PF * l;

        return P / dp;
    }

    double area(double ax, double ay, double bx, double by, double cx, double cy) {
        return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax);
    }

    boolean bounding(double a, double b, double c, double d) {
        if (a > b) {
            double t = a;
            a = b;
            b = t;
        }
        if (c > d) {
            double t = c;
            c = d;
            d = t;
        }
        return Math.max(a, c) <= Math.min(b, d);
    }

    boolean intersect(double ax, double ay, double bx, double by, double cx, double cy) {
        return bounding(ax, bx, cx, 0)
                && bounding(ay, by, cy, 0)
                && area(ax, ay, bx, by, cx, cy) * area(ax, ay, bx, by, 0, 0) <= 0
                && area(cx, cy, 0, 0, ax, ay) * area(cx, cy, 0, 0, bx, by) <= 0;
    }

    long P, Q;
    long PF, QF;

    void solve() throws IOException {
        int n = readInt();
        P = readInt();
        Q = readInt();

        List<Point> input = new ArrayList<>();
        long maxX = 0;
        long maxY = 0;
        for (int i = 0; i < n; i++) {
            Point p = new Point(readInt(), readInt());
            input.add(p);
            maxX = Math.max(maxX, p.x);
            maxY = Math.max(maxY, p.y);
        }
        input.add(new Point(0, maxY));
        input.add(new Point(maxX, 0));

        List<Point> pts = convex(input.toArray(new Point[input.size()]));


        long multiple = ((long) 1e9) / Math.max(P, Q);
        PF = P * multiple;
        QF = Q * multiple;

        double time = Double.MAX_VALUE;
        for (Point p : pts) {
            time = Math.min(time(p), time);
        }

        for (int i = 0; i < pts.size(); i++) {
            int next = (i + 1) % pts.size();
            time = Math.min(time, time(pts.get(i), pts.get(next)));
        }
        out.println(time);


    }

}