Problem: Andrey needs one more problem to conduct a programming contest. He has n friends who are always willing to help. He can ask some of them to come up with a contest problem. Andrey knows one value for each of his fiends — the probability that this friend will come up with a problem if Andrey asks him.

Help Andrey choose people to ask. As he needs only one problem, Andrey is going to be really upset if no one comes up with a problem or if he gets more than one problem from his friends. You need to choose such a set of people that maximizes the chances of Andrey not getting upset.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of Andrey's friends. The second line contains n real numbers pi (0.0 ≤ pi ≤ 1.0) — the probability that the i-th friend can come up with a problem. The probabilities are given with at most 6 digits after decimal point.

Output

Print a single real number — the probability that Andrey won't get upset at the optimal choice of friends. The answer will be considered valid if it differs from the correct one by at most 10 - 9.

Examples

Input

4
0.1 0.2 0.3 0.8


Output

0.800000000000


Input

2
0.1 0.2


Output

0.260000000000

Note

In the first sample the best strategy for Andrey is to ask only one of his friends, the most reliable one.

In the second sample the best strategy for Andrey is to ask all of his friends to come up with a problem. Then the probability that he will get exactly one problem is 0.1·0.8 + 0.9·0.2 = 0.26.

Solution (in JAVA):

Solution:

import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class B442 
{

	public static int mod = 1000000007;
	public static long INF = (1L << 60);
	static FastScanner2 in = new FastScanner2();
	static OutputWriter out = new OutputWriter(System.out);
 
	public static void main(String[] args) 
	{

		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		double[] p=new double[n];
		for(int i=0;i<n;i++)
		{
			p[i]=sc.nextDouble();
		}
		Arrays.sort(p);
		double P=1,S=0;
		for(int i=n-1;i>=0;i--)
		{
			if(p[i]==1)
			{
				System.out.println(p[i]);
				return;
			}
			if(S<1)
			{
				S+=(p[i])/(1-p[i]);
				P*=(1-p[i]);
			}
			else
			{
				break;
			}
		}
		out.println(P*S);
		out.close();

	}
	
	public static long pow(long x, long n) 
	{
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p)) 
		{
			if ((n & 1) != 0) 
			{
				res = (res * p);
			}
		}
		return res;
	}
	
	public static long pow(long x, long n, long mod) 
	{
		long res = 1;
		for (long p = x; n > 0; n >>= 1, p = (p * p) % mod) 
		{
			if ((n & 1) != 0) 
			{
				res = (res * p % mod);
			}
		}
		return res;
	}

	public static long gcd(long n1, long n2)
	{
		long r;
		while (n2 != 0) 
		{
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long lcm(long n1, long n2) 
	{
		long answer = (n1 * n2) / (gcd(n1, n2));
		return answer;
	}
	
	static class FastScanner2 
	{
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() 
		{
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) 
			{
				curChar = 0;
				try 
				{
					snumChars = System.in.read(buf);
				} catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} 
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} 
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n)
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n)
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}
	}

	static class InputReader 
	{
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream inputstream) 
		{
			reader = new BufferedReader(new InputStreamReader(inputstream));
			tokenizer = null;
		}

		public String nextLine() 
		{
			String fullLine = null;
			while (tokenizer == null || !tokenizer.hasMoreTokens())
			{
				try 
				{
					fullLine = reader.readLine();
				} catch (IOException e)
				{
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}

		public String next()
		{
			while (tokenizer == null || !tokenizer.hasMoreTokens()) 
			{
				try 
				{
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) 
				{
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

		public int[] nextIntArray(int n) 
		{
			int a[] = new int[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n)
		{
			long a[] = new long[n];
			for (int i = 0; i < n; i++) 
			{
				a[i] = nextLong();
			}
			return a;
		}

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

	static class OutputWriter 
	{
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) 
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects)
		{
			for (int i = 0; i < objects.length; i++) 
			{
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println(Object... objects)
		{
			print(objects);
			writer.println();
		}

		public void close() 
		{
			writer.close();
		}

		public void flush() 
		{
			writer.flush();
		}
	}
private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
	private static void debug(Object... o) 
	{
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
	private static void tr(Object... o) 
	{
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}