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.IOException;
import java.util.Arrays;
import java.io.FilterInputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedInputStream;
import java.io.InputStream;

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

class TaskB {
    public void solve(int testNumber, JoltyScanner in, PrintWriter out) {
        int n = in.nextInt();
        double[] chances = new double[n];
        for (int i = 0; i < n; i++) {
            chances[i] = in.nextDouble();
        }
        Arrays.sort(chances);
        double success = 0;
        double none = 1.0;
        for (int i = n - 1; i >= 0; i--) {
            double next = none * chances[i] + success * (1 - chances[i]);
            if (next <= success) {
                break;
            }
            success = next;
            none *= (1 - chances[i]);
        }
        out.printf("%.12f%n", success);
    }
}

class JoltyScanner {
    public static final int BUFFER_SIZE = 1 << 16;
    public static final char NULL_CHAR = (char) -1;

    StringBuilder str = new StringBuilder();
    byte[] buffer = new byte[BUFFER_SIZE];
    boolean EOF_FLAG = false;
    int bufferIdx = 0, size = 0;
    char c = (char) -1;
    BufferedInputStream in = new BufferedInputStream(System.in, BUFFER_SIZE);
    public JoltyScanner(InputStream in) {
        this.in = new BufferedInputStream(in);
    }
    public int nextInt() {
        long x = nextLong();
        if (x > Integer.MAX_VALUE || x < Integer.MIN_VALUE) {
            throw new ArithmeticException("Scanned value overflows integer");
        }
        return (int) x;
    }
    public long nextLong() {
        boolean negative = false;
        if (c == NULL_CHAR) {
            c = nextChar();
        }
        while (!EOF_FLAG && (c < '0' || c > '9')) {
            if (c == '-') {
                negative = true;
            }
            c = nextChar();
        }
        if (EOF_FLAG) {
            throw new EndOfFileException();
        }
        long res = 0;
        while (c >= '0' && c <= '9') {
            res = (res << 3) + (res << 1) + c - '0';
            c = nextChar();
        }
        return negative ? -res : res;
    }
    public String next() {
        if (EOF_FLAG) {
            throw new EndOfFileException();
        }
        if (c == NULL_CHAR) {
            c = nextChar();
        }
        while (!EOF_FLAG && Character.isWhitespace(c)) {
            c = nextChar();
        }
        str.setLength(0);
        while (!EOF_FLAG && !Character.isWhitespace(c)) {
            str.append(c);
            c = nextChar();
        }
        return str.toString();
    }
    public char nextChar() {
        if (EOF_FLAG) {
            return NULL_CHAR;
        }
        while (bufferIdx == size) {
            try {
                size = in.read(buffer);
                if (size == -1) {
                    throw new Exception();
                }
            }
            catch (Exception e) {
                EOF_FLAG = true;
                return (char) -1;
            }
            if (size == -1) {
                size = BUFFER_SIZE;
            }
            bufferIdx = 0;
        }
        return (char) buffer[bufferIdx++];
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public class EndOfFileException extends RuntimeException {}
}