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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class C_Round_335_Div1 {

	public static long MOD = 1000000007;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int p = in.nextInt();
		int q = in.nextInt();
		final Point[] data = new Point[n + 2];
		double maxX = 0;
		double maxY = 0;
		for (int i = 1; i <= n; i++) {

			data[i] = new Point(in.nextInt(), in.nextInt());
			maxX = Math.max(maxX, data[i].x);
			maxY = Math.max(maxY, data[i].y);
		}
		data[0] = new Point(maxX, 0);
		data[n + 1] = new Point(0, maxY);

		Arrays.sort(data, 1, n + 2, new Comparator<Point>() {

			@Override
			public int compare(Point o1, Point o2) {
				int orient = orientation(data[0], o1, o2);
				if (orient == 0) {
					return Double.compare(distSq(data[0], o1),
							distSq(data[0], o2));
				}

				return (orient == 2) ? -1 : 1;
			}
		});
		Point[] stack = new Point[n + 2];
		int cur = 0;
		for (int i = 0; i < data.length; i++) {
			while (cur > 2
					&& orientation(stack[cur - 2], stack[cur - 1], data[i]) != 2) {
				cur--;
			}
			stack[cur++] = data[i];
		}
		//System.out.println(Arrays.toString(stack));
		Line pq = getLine(new Point(0, 0), new Point(p, q));
		double result = Double.MAX_VALUE;
		for (int i = 0; i < cur; i++) {
			int nxt = (i + 1) % cur;
			//System.out.println(stack[i] + " " + stack[nxt]);
			Line other = getLine(stack[i], stack[nxt]);
			double[] tmp = intersect(other, pq);
			//System.out.println(Arrays.toString(tmp));
			if (tmp != null) {
				if ((stack[i].x <= tmp[0] && tmp[0] <= stack[nxt].x)
						|| (stack[i].x >= tmp[0] && tmp[0] >= stack[nxt].x)) {
					if ((stack[i].y <= tmp[1] && tmp[1] <= stack[nxt].y)
							|| (stack[i].y >= tmp[1] && tmp[1] >= stack[nxt].y)) {
						result = Math.min(result, (double) p / tmp[0]);
					}
				}
				result = Math.min(
						result,
						Math.max((double) p / stack[i].x, (double) q
								/ stack[i].y));
				result = Math.min(
						result,
						Math.max((double) p / stack[nxt].x, (double) q
								/ stack[nxt].y));
			}
		}
		out.println(result);

		out.close();
	}

	static double[] intersect(Line a, Line b) {

		double det = a.a * b.b - b.a * a.b;
		if (det == 0) {
			return null;
		} else {
			double x = (b.b * a.c - a.b * b.c) / det;
			double y = (a.a * b.c - b.a * a.c) / det;
			return new double[] { x, y };
		}

	}

	static Line getLine(Point a, Point b) {
		if (a.x == b.x) {
			return new Line(1, 0, a.x);
		} else {
			double m = (a.y - b.y) / (a.x - b.x);
			double x = a.y - m * a.x;
			return new Line(-m, 1, x);
		}
	}

	static class Line {
		double a, b, c;

		public Line(double a, double b, double c) {
			super();
			this.a = a;
			this.b = b;
			this.c = c;
		}

	}

	static double distSq(Point p1, Point p2) {
		return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
	}

	// To find orientation of ordered triplet (p, q, r).
	// The function returns following values
	// 0 --> p, q and r are colinear
	// 1 --> Clockwise
	// 2 --> Counterclockwise
	static int orientation(Point p, Point q, Point r) {
		double val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);

		if (val == 0)
			return 0; // colinear
		return (val > 0) ? 1 : 2; // clock or counterclock wise
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point {

		double x, y;

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

		@Override
		public String toString() {
			return "Point [x=" + x + ", y=" + y + "]";
		}

	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}