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.util.*;
		import java.math.*;
		
		 
		 public class Main	{
		   static class Pair implements Comparable<Pair>{
		   int a;
		   int b;
		   public Pair(){}
		   public Pair(int x,int y){a=x;b=y;}
		   public int compareTo(Pair p){
			 return Integer.compare(a, p.a);
		   }
	//	   long a,b;
	//	   public Pair(long x,long y){a=x;b=y;}
	//	   public int compareTo(Pair p){
	//			 return Long.compare(a, p.a);
	//	   }
	//	  
	//	@Override
	//	public int hashCode() {
	//		final int prime = 31;
	//		int result = 1;
	//		result = prime * result + a;
	//		result = prime * result + b;
	//	//	out.println("hashcode = "+result);
	//		return result;
	//	}
	//	@Override
	//	public boolean equals(Object obj) {
	//		Pair cur = (Pair)obj;
	//		if((a==cur.a && b==cur.b) || (a==cur.b && b==cur.a))return true;
	//		return false;
	//	}
		 }
	
		   static class cell implements Comparable<cell>{
			   int a,b;
			   long dis;
			   public cell(int x,int y,long z) {a=x;b=y;dis=z;}
			   public int compareTo(cell c) {
				   return Long.compare(dis,c.dis);
			   }
		   }
		static class TrieNode{
			TrieNode left;
			TrieNode right;
			int op;
			int data;
			public TrieNode() {}
		}
		  public static int gcd(int a,int b)
		  {
		    if(a<b)
		
		      return gcd(b,a);
		    if(b==0)
		      return a;
		    return gcd(b,a%b);
		    
		  }
		  static int lcm(int a,int b) {
			  return  a*b / gcd(a,b);
		  }
		  //static long ans = 0;
		  static long mod = (long)(1e9+7); //998244353;//
		   
		    public static void main(String[] args) throws Exception {
		       new Thread(null, null, "Anshum Gupta", 99999999) {
		            public void run() {
		                try {
		                    solve();
		                } catch(Exception e) {
		                    e.printStackTrace();
		                    System.exit(1);
		                }
		            }
		        }.start();
		    }
		
		static long pow(long x,long y){
		    if(y == 0)return 1;
		    if(y==1)return x;
		    long a = pow(x,y/2);
		    a = (a*a)%mod;
		    if(y%2==0){
		        return a;
		    }
		    return (a*x)%mod;
		}
		
		static long mxx;
		static int mxN = (int)(2e6+5);
		static long[]fact,inv_fact;
		static long my_inv(long a) {
			return pow(a,mod-2);
		}
		static long bin(int a,int b) {
			if(a < b || a<0 || b<0)return 0;
		    return ((fact[a]*inv_fact[a-b])%mod * inv_fact[b])%mod;
		}
	//	static ArrayList<ArrayList<Integer>>adj;
	//	static boolean[]vis;
		static void make_facts() {
		  fact=new long[mxN];
		  inv_fact = new long[mxN];
		  fact[0]=inv_fact[0]=1L;
		  for(int i=1;i<mxN;i++) {
			   fact[i] = (i*fact[i-1])%mod;
			   inv_fact[i] = my_inv(fact[i]);
		  }
		}
		//static int[]bfs(int a){
		//	Queue<Integer> q = new  LinkedList<Integer>();
		//	
		//	vis = new boolean[n+1];
		//	int[]dis = new int[n+1];
		//	q.add(a);
		//	dis[a] = 0;
		//	vis[a] = true;
		//	while(!q.isEmpty()) {
		//		int cur = q.poll();
		//	//	vis[cur] = true;
		//	//	if(cur == b)break;
		//		for(int x : adj.get(cur)) {
		//			if(vis[x])continue;
		//			q.add(x);
		//			dis[x] = dis[cur]+1;
		//			vis[x] = true;
		//		}
		//	}
		//	return dis;
		//}
		
		 public static void solve() throws Exception {
		   // solve the problem here
		   MyScanner s = new MyScanner();
		        out = new PrintWriter(new BufferedOutputStream(System.out), true);
		        int tc = 1;//s.nextInt();
		        mxx = (long)(1e18+5);
	//	        make_facts(); 
	//	        int mod = (int)1e9+7;
		        while(tc-->0){
		        	int n = s.nextInt();
		        	Double[] p = new Double[n];
		        	for(int i=0;i<n;i++)p[i] = s.nextDouble();
		        	Arrays.sort(p, Collections.reverseOrder());
		        	double ans = 0;
		        	
		        		for(int k=1;k<=n;k++) {
		        			double cur = 0;
		        			for(int i=0;i<k;i++) {
			        			double prod = 1;
			        			for(int j=0;j<k;j++) {
			        				if(i!=j)prod *= (1-p[j]);
			        			}
			        			cur += prod * p[i];
			        		}
		        			ans = Math.max(ans, cur);
		        		}
		        		
		        	
		        	out.println(ans);
		        }
		        	
		           
		        out.flush();
		}
		 
		     
		 
		 
		 
		    //-----------PrintWriter for faster output---------------------------------
		    public static PrintWriter out;
		 
		    //-----------MyScanner class for faster input----------
		    public static class MyScanner {
		        BufferedReader br;
		        StringTokenizer st;
		 
		        public MyScanner() {
		            br = new BufferedReader(new InputStreamReader(System.in));
		        }
		 
		        String next() {
		            while (st == null || !st.hasMoreElements()) {
		                try {
		                    st = new StringTokenizer(br.readLine());
		                } catch (IOException e) {
		                    e.printStackTrace();
		                }
		            }
		            return st.nextToken();
		        }
		 
		        int nextInt() { return Integer.parseInt(next()); }
		        long nextLong() { return Long.parseLong(next()); }
		        double nextDouble() { return Double.parseDouble(next()); }
		         
		        String nextLine(){
		            String str = "";
		            try {
		                str = br.readLine();
		            } catch (IOException e) {
		                e.printStackTrace();
		            }
		            return str;
		        }
		    }
		    //--------------------------------------------------------
		}