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 project {
	public static void main(String[] args) throws IOException {
		input.init(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = input.nextInt();
		double p = input.nextInt(), q = input.nextInt();
		double[] as = new double[n], bs = new double[n];
		for(int i = 0; i<n; i++)
		{
			as[i] = input.nextInt();
			bs[i] = input.nextInt();
		}
		out.println(dual(n, p, q, as, bs));
		out.close();
	}
	static double dual(int n, double p, double q, double[] as, double[] bs)
	{
		double lo = 0, hi = 1e9;
		for(int i = 0; i<n; i++) hi = Math.min(hi, 1.0/as[i]);
		for(int iter = 0; iter < 40; iter++)
		{
			double m1 = (lo+lo+hi)/3, m2 = (lo + hi+hi)/3;
			double f1 = f(p, q, as, bs, m1), f2 = f(p, q, as, bs, m2);
			if(f1 < f2) lo = m1;
			else hi = m2;
		}
		return f(p, q, as, bs, (lo+hi)/2);
	}
	static double f(double p, double q, double[] as, double[] bs, double y1)
	{
		double y2 = (1 - as[0] * y1) / bs[0];
		for(int i = 1; i<as.length; i++) y2 = Math.min(y2, (1 - as[i] * y1) / bs[i]);
		return p * y1 + q * y2;
	}
	static double simplex(int n, double p, double q, double[] as, double[] bs)
	{
		double[] c = new double[n];
		Arrays.fill(c, -1);
		double[] b = new double[]{-p, -q};
		double[][] a = new double[2][n];
		for(int i = 0; i<n; i++)
		{
			a[0][i] = -as[i];
			a[1][i] = -bs[i];
		}
		LPSolver lp = new LPSolver(a, b, c);
		double res = lp.Solve();
		return -res;
	}
	
	/*
	Simplex Method
	Maximize c^T x subject to   Ax <= b, x >= 0
	INPUT: A -- an m x n matrix, b -- an m-dimensional vector, c -- an n-dimensional vector, x -- a vector where the optimal solution will be stored
	OUTPUT: value of the optimal solution (infinity if unbounded above, nan if infeasible)
	To use this code, create an LPSolver object with A, b, and c as arguments.  Then, call Solve().
	*/
	static class LPSolver 
	{
		static double eps = 1e-9, oo = 987654321;
		int m, n;
		int[] B, N;
		double[][] D;
		LPSolver(double[][] A, double[] b, double[] c)
		{	
			m = b.length; n = c.length; N = new int[n+1]; B = new int[m]; D = new double[m+2][n+2];
		    for (int i = 0; i < m; i++) for(int j = 0; j < n; j++) D[i][j] = A[i][j];
		    for (int i = 0; i < m; i++) 
		    {
		    	B[i] = n+i; 
		    	D[i][n] = -1; 
		    	D[i][n+1] = b[i]; 
		    }
		    for (int j = 0; j < n; j++) D[m][j] = -c[N[j]=j]; 
		    D[m+1][n] = -(N[n]=-1);
		}
			   
		void Pivot(int r, int s) 
		{
			for (int i = 0; i < m+2; i++) if (i != r)
				for (int j = 0; j < n+2; j++) if (j != s)
					D[i][j] -= D[r][j] * D[i][s] / D[r][s];
		    for (int j = 0; j < n+2; j++) if (j != s) D[r][j] /= D[r][s];
		    for (int i = 0; i < m+2; i++) if (i != r) D[i][s] /= -D[r][s];
		    D[r][s] = 1.0 / D[r][s];
		    B[r] = (N[s] = (B[r] = B[r] ^ N[s]) ^ N[s]) ^ B[r];
		  }

		  boolean Simplex(int phase) 
		  {
			  int x = phase == 1 ? m+1 : m;
			  while (true) 
			  {
				  int s = -1;
				  for (int j = 0; j <= n; j++) 
					  if ((phase != 2 || N[j] != -1) && (s == -1 || D[x][j] < D[x][s] || D[x][j] == D[x][s] && N[j] < N[s])) s = j;
				  if (D[x][s] >= -eps) return true;
				  int r = -1;
				  for (int i = 0; i < m; i++) 
				  {
					  if (D[i][s] < eps) continue;
					  if (r == -1 || D[i][n+1] / D[i][s] < D[r][n+1] / D[r][s] || D[i][n+1] / D[i][s] == D[r][n+1] / D[r][s] && B[i] < B[r]) r = i;
				  }
				  if (r == -1) return false;
				  Pivot(r, s);
			  }
		  }

		  double Solve() 
		  {
			  int r = 0;
			  for (int i = 1; i < m; i++) if (D[i][n+1] < D[r][n+1]) r = i;
			  if (D[r][n+1] <= -eps) 
			  {
				  Pivot(r, n);
				  if (!Simplex(1) || D[m+1][n+1] < -eps) return -oo;
				  for (int i = 0; i < m; i++) if (B[i] == -1) 
				  {
					  int s = -1;
					  for (int j = 0; j <= n; j++) if (s == -1 || D[i][j] < D[i][s] || D[i][j] == D[i][s] && N[j] < N[s]) s = j;
					  Pivot(i, s);
				  }
			  }
			  if (!Simplex(2)) return oo;
			  double[] x = new double[n];
			  for (int i = 0; i < m; i++) if (B[i] < n) x[B[i]] = D[i][n+1];
			  return D[m][n+1];
		  }
	}
	
	public static class input {
		static BufferedReader reader;
		static StringTokenizer tokenizer;

		static void init(InputStream input) {
			reader = new BufferedReader(new InputStreamReader(input));
			tokenizer = new StringTokenizer("");
		}

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

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

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

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