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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AlexFetisov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE_Points solver = new TaskE_Points();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE_Points {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            PP T = new PP(in);
            PP[] points = new PP[n];
            long maxX = 0, maxY = 0;
            for (int i = 0; i < n; ++i) {
                points[i] = new PP(in);
                maxX = Math.max(points[i].x, maxX);
                maxY = Math.max(points[i].y, maxY);
            }
            Arrays.sort(points);
            List<PP> pp2 = new ArrayList<PP>();
            pp2.add(points[0]);
            for (int i = 1; i < points.length; ++i) {
                if (!pp2.get(pp2.size() - 1).eq(points[i])) {
                    pp2.add(points[i]);
                }
            }
            points = new PP[pp2.size()];
            for (int i = 0; i < pp2.size(); ++i) {
                points[i] = pp2.get(i);
            }

            List<PP> convex = new ArrayList<PP>();
            convex.add(new PP(0, maxY));
            for (PP p : points) {
                while (convex.size() >= 2 && crossProd(
                    convex.get(convex.size() - 2), convex.get(convex.size() - 1), p) > 0) {
                    convex.remove(convex.size() - 1);
                }
                convex.add(p);
            }
            convex.add(new PP(maxX, 0));

            double best = 1e100;
            for (int i = 1; i < convex.size(); ++i) {
                Segment s2 = new Segment(convex.get(i - 1).t(), convex.get(i).t());
                Point p = new Line(
                    convex.get(i - 1).t(), convex.get(i).t()).intersect(
                    new Line(new PP(0, 0).t(), T.t()));
                if (p == null) continue;
                if (!s2.contains(p, true)) continue;
                best = Math.min(best, T.x / p.x);
                best = Math.min(best, T.y / p.y);
            }
            out.println(best);
        }

        private double crossProd(PP A, PP B, PP C) {
            PP AA = new PP(B.x - A.x, B.y - A.y);
            PP BB = new PP(C.x - A.x, C.y - A.y);
            return Long.signum(AA.x * BB.y - AA.y * BB.x);
        }

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

            Point t() {
                return new Point(x, y);
            }

            boolean eq(PP p) {
                return x == p.x && y == p.y;
            }

            public PP(InputReader in) {
                x = in.nextInt();
                y = in.nextInt();
            }

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


            public int compareTo(PP o) {
                if (x != o.x) return Long.signum(x - o.x);
                return Long.signum(y - o.y);
            }

        }

    }

    static class Line {
        public final double a;
        public final double b;
        public final double c;
        public Point p1;
        public Point p2;
        boolean hasPoints;


        public int hashCode() {
            double res = a * 1e50 + b * 1e25 + c;
            return (int) res;
        }

        public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
            p1 = p2 = null;
            hasPoints = false;
        }

        public Line(double a, double b, double c) {
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = false;
        }

        public Line(Point p1, Point p2) {
            double a = p2.y - p1.y;
            double b = p1.x - p2.x;
            double c = -(p1.x * a + p1.y * b);
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = true;
        }

        public Point intersect(Line other) {
            if (parallel(other)) {
                return null;
            }
            double determinant = b * other.a - a * other.b;
            double x = (c * other.b - b * other.c) / determinant;
            double y = (a * other.c - c * other.a) / determinant;
            return new Point(x, y);
        }

        public boolean parallel(Line other) {
            return DoubleUtils.compareTo(Math.abs(a * other.b - b * other.a), 0) == 0;
        }

        public boolean contains(Point point) {
            return DoubleUtils.compareTo(Math.abs(value(point)), 0) == 0;
        }

        public Line perpendicular(Point point) {
            return new Line(-b, a, b * point.x - a * point.y);
        }

        public double value(Point point) {
            return a * point.x + b * point.y + c;
        }


        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Line line = (Line) o;

            if (!parallel(line)) return false;
            if (Math.abs(a * line.c - c * line.a) > DoubleUtils.EPS || Math.abs(b * line.c - c * line.b) > DoubleUtils.EPS)
                return false;

            return true;
        }

    }

    static class Segment {
        public final Point a;
        public final Point b;
        private Line line = null;

        public Segment(Point a, Point b) {
            this.a = a;
            this.b = b;
        }

        public boolean contains(Point point, boolean withEnds) {
            if (a.equals(point) || b.equals(point)) {
                return withEnds;
            }
            if (a.equals(b)) {
                return false;
            }
            Line line = line();
            if (!line.contains(point)) {
                return false;
            }
            Line perpendicular = line.perpendicular(a);
            double aValue = perpendicular.value(a);
            double bValue = perpendicular.value(b);
            double pointValue = perpendicular.value(point);
            return aValue < pointValue && pointValue < bValue || bValue < pointValue && pointValue < aValue;
        }


        public String toString() {
            return a.toString() + ", " + b.toString();
        }

        public Line line() {
            if (line == null) {
                line = a.line(b);
            }
            return line;
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String nextString() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

        public double nextDouble() {
            return Double.parseDouble(nextString());
        }

    }

    static class Point implements Comparable<Point> {
        public double x;
        public double y;

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

        public Line line(Point other) {
            if (equals(other))
                return null;
            double a = other.y - y;
            double b = x - other.x;
            double c = -a * x - b * y;
            return new Line(a, b, c);
        }

        public Point() {
            this.x = 0;
            this.y = 0;
        }

        public Point(InputReader in) {
            this.x = in.nextDouble();
            this.y = in.nextDouble();
        }


        public String toString() {
            return "(" + x + ", " + y + " )";
        }


        public boolean equals(Object o) {
            Point p = (Point) o;
            return DoubleUtils.compareTo(x, p.x) == 0 && DoubleUtils.compareTo(y, p.y) == 0;
        }


        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }


        public int compareTo(Point o) {
            int temp = DoubleUtils.compareTo(x, o.x);
            if (temp == 0) {
                return DoubleUtils.compareTo(y, o.y);
            }
            return temp;
        }

    }

    static class DoubleUtils {
        public static final double EPS = 1e-8;

        public static double sqr(double x) {
            return x * x;
        }

        public static int compareTo(double a, double b) {
            if (doubleEqual(a, b)) {
                return 0;
            }
            if (a < b) {
                return -1;
            }
            return 1;
        }

        private static boolean doubleEqual(double a, double b) {
            return Math.abs(a - b) < EPS;
        }

        public static double sqrt(double a) {
            if (compareTo(a, 0) < 0) {
                System.exit(1);
            }
            if (a < 0) return 0;
            return Math.sqrt(a);
        }

        public static double hypot(double a, double b) {
            return sqrt(sqr(a) + sqr(b));
        }

    }
}