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.awt.List;
		import java.io.*;
		import java.util.*;
		
		
		
		
		/*
		 * 
		 * daiict
		 *
		 * 
		 * 
		 */
		
		
		public class Main {
			FastScanner in;
			PrintWriter out;
		
			static ArrayList[] adj;
			static ArrayList[] obj;
			static int n;
			static int x;
			static int c;
			static int visited[];
			static int Ad[];
			static int Bd[];
			static double ans = 0;
			static int brr[][];
			static int a;
			static int b;
			static int parent[];
			static int size[];
			long mod = (long)1e9+7;
			static int ds[];
			
		//Segment tree do not delete
			static int arr[];	
			static int d[];
			static int h;
		// till now	
		
			class Segment{
			  private  int Lazy[];
			 
			    void ans(){
			   
			    	
			     int x = (int) (Math.ceil(Math.log(100000) / Math.log(2)));
			        int max_size = 2 * (int) Math.pow(2, x) - 1;
			        int SegTree[][] = new int[max_size][3]; // allocate memory
			        Lazy = new int[max_size];
			        
			       String s = in.next();
			       n = s.length();
			        
			        int q=in.nextInt();
			        
		
			        build_ST(0, 0, n - 1,SegTree,s);
			  
			        for(int i = 0;i<2*n;i++){
			        	System.out.println(SegTree[i][0] + " " + SegTree[i][1] + " " + SegTree[i][2] + " " + (i+n));
			        }
			        
			        while(q-->0)
			        {
			          int a = in.nextInt();
			          int b = in.nextInt();
			          
			          int d = getMaxST(0, n-1, a-1, b-1, 0,SegTree);
			          System.out.println(d);
			        }
			    }
			    
			    
			 void build_ST(int node, int start, int end,int SegTree[][],String s) 
			   {
			    if(start > end) return; 
			  	if(start == end) { 
			  		System.out.println(start + " " + node);
			  		if(s.charAt(start) == '('){
			  			SegTree[node][1] = 1;
			  		}else{
			  			SegTree[node][2] = 1;
			  		}
			  		
					return;
				}
				int mid=(start + end) >> 1;
				build_ST(node*2+1, start, mid, SegTree,s); // Init left child
				build_ST(node*2+2, 1+mid, end,SegTree,s); // Init right child
				
				// Init root value
				
				int t = Math.min(SegTree[2*node + 1][1], SegTree[2*node+2][2]);
				
				SegTree[node][0] = SegTree[2*node+1][0] + SegTree[2*node+2][0] + 2*t;
				SegTree[node][1] = SegTree[2*node+1][1] + SegTree[2*node+2][1] - t;
				SegTree[node][2] = SegTree[2*node+1][2] + SegTree[2*node+2][2] - t;
				
				
			}
		//	    void update_ST(int node, int start, int end, int l, int r, int diff) {
		//	        if(Lazy[node] != 0)
		//	        {
		//	            int pending = Lazy[node];
		//	            
		//	            SegTree[node] -= pending;
		//	            
		//	           if(start != end)
		//	            {
		//	                Lazy[2 * node + 1] += Lazy[node];
		//	                Lazy[2 * node + 2] += Lazy[node];
		//	            }
		//	           Lazy[node] = 0;
		//	        }
		//	        if (end < l || start > r)
		//	            return ;
		//	          if(l<=start && end<=r)
		//	        {
		//	        	  SegTree[node] -= diff;
		//	               
		//	            if(start != end) // not a leaf
		//	            {
		//	                Lazy[2*node+1] += diff;
		//	                Lazy[2*node+2] += diff;
		//	            }
		//	            return;
		//	        }
		//	        int mid=(start + end) >> 1;
		//		update_ST(node*2+1, start, mid, l, r, diff); // Updating left child
		//		update_ST(2+node*2, 1+mid, end, l, r, diff); // Updating right child
		//	
		//		SegTree[node] = Math.max(SegTree[node*2+1],SegTree[node*2+2]); 
		//		
		//	    }
			      int getMaxST(int start, int end, int l, int r, int node,int SegTree[][])
			    {
		//	    	  if(Lazy[node] != 0)
		//		        {
		//		            int pending = Lazy[node];
		//		            
		//		            SegTree[node] -= pending;
		//		            
		//		           if(start != end)
		//		            {
		//		                Lazy[2 * node + 1] += Lazy[node];
		//		                Lazy[2 * node + 2] += Lazy[node];
		//		            }
		//		           Lazy[node] = 0;
		//		        }
			        if (l <= start && r >= end)
			            return SegTree[node][0];
			         if (end < l || start > r)
			            return 0;
			        int mid = (start + end) >> 1;
			        return getMaxST(start, mid, l, r, 2 * node + 1,SegTree)+getMaxST(mid + 1, end, l, r, 2 * node + 2,SegTree);
			    }
			      
			}
			
			static class Pair implements Comparable<Pair>
		    {
				int x;int y;
				
		        Pair(int l, int m) {
		          
		        	this.x = l;
		            this.y = m;
		           
		        }
		        
		        public int compareTo(Pair p) {
		            if (this.x == p.x) {
		                return (int)(this.y-p.y);
		            }
		            return (int)(this.x - p.x);
		        }
		        
		        public String toString(){
		        	return x + " " + y;
		        }
		        
		        public boolean equals(Object o){
		        	if(o instanceof Pair){
		        		Pair a = (Pair)o;
		        		
		        		return this.x == a.x && this.y == a.y;
		        	}
		        	
		        	return false;
		        }
		        
		        public int hashCode(){
		        	return new Long(x).hashCode()*31 + new Long(y).hashCode();
		        }
		    
		    }
		    
			
			public static int gcd(int a, int b) {
				if (b == 0) return a;
				return gcd(b, a%b);
			}
			
			public static int find(int i){
				if(parent[i] != i){
					return find(parent[i]);
				}
				
				return i;
			}
			
			
			public static void union(int a,int b){
				int ra = find(a);
				int rb = find(b);
		
				if(ra!= rb){
					if(size[ra] > size[rb]){
						parent[rb] =ra;
						size[ra] += size[rb];
					}else{
						parent[ra] = rb;
						size[rb] += size[ra];
					}
				}
				
			}
		
			public static void apply(int p,int value){
				arr[p] += value;
				
				if(p < n){
					d[p] += value;
				}
			}
			
			public static void push(int p){
				
				for(int s = h;s>0;s--){
					int i = p >> s;
					
					if(d[i] != 0){
						apply(i<<1,d[i]);
						apply(i<<1|1,d[i]);
						d[i] = 0;
					}		
				}		
			}
			
			public static void lazybuild(int p){
				while(p > 1){
					p>>=1;
					arr[p] = Math.max(arr[p<<1], arr[p<<1|1]) + d[p];
				}
			}
			
			public static void lazyupdate(int l,int r,int value){
				l += n; r += n+1;		
				int l0 = l;int r0 = r;
				for(;l<r; l>>=1,r>>=1){
					if((l&1) == 1){
						apply(l++,value);
					}
					
					if((r&1) == 1){
						apply(--r,value);
					}
				}
				lazybuild(l0);
				lazybuild(r0-1);
					
			}
			
			public static int lazyquery(int l,int r){
				l += n;r += n+1;
				push(l);push(r-1);
				int res = (int)-2e9;
				
				for(;l<r;l>>=1,r>>=1){
					if((l&1) == 1){
						res = Math.max(arr[l++], res);
					}
					
					if((r&1) == 1){
						res = Math.max(arr[--r], res);
					}
				}
				
				return res;
			}
			
			public static void build(){
				
				for(int i = n-1;i>0;i--){
					arr[i] = Math.max(arr[i<<1], arr[i<<1|1]);
				}
				
			}
			
			public static void update(int p,int v){
				
				for(arr[p += n] = v; p>0; p>>=1 ){
					arr[p>>1] = Math.max(arr[p], arr[p^1]);
				}
				
			}
			
			public static int query(int l,int r){
				
				r++;
				int max = 0;
				for(l +=n,r +=n;l<r; l>>=1,r>>=1 ){
					
				
					
					if((l&1) == 1){
						max = Math.max(max, arr[l++]);
					}
					
					if((r&1) == 1){
						max = Math.max(max, arr[--r]);
					}
				}
				
				return max;
			}
			
			void multiply(long a[][], long b[][])
			{
			    
			    long mul[][] = new long[3][3];
			    for (int i = 0; i < 3; i++)
			    {
			        for (int j = 0; j < 3; j++)
			        {
			            mul[i][j] = 0;
			            for (int k = 0; k < 3; k++)
			                mul[i][j] = (int) ((mul[i][j] + (a[i][k]*b[k][j])%mod)%mod);
			        }
			    }
			 
			  
			    for (int i=0; i<3; i++)
			        for (int j=0; j<3; j++)
			            a[i][j] = mul[i][j];  
			}
			
			long power(long F[][], long n)
			{
			    long M[][] = {{1,1,0}, {1,0,0}, {0,1,0}};
			 
			    if (n==1)
			        return (long) ((F[0][0] + F[0][1])%mod);
			 
			    power(F, n/2);
			 
			    multiply(F, F);
			 
			    if (n%2 != 0)
			        multiply(F, M);
			 
			    return (long) ((F[0][0] + F[0][1])%mod) ;
			}
			 
			
			long findNthTerm(long n)
			{
			    long[][] F = {{1,1,0}, {1,0,0}, {0,1,0}} ;
			 
			    return power(F, n);
			}
			 
			
			
		    void solve() throws NumberFormatException, IOException {
		 
		    	Scanner in = new Scanner(System.in);
		    
		    	int n = in.nextInt();
		    	in.nextLine();
		    	
		    	double arr[] = new double[n];
		    	double temp[] = new double[n];
		    	
		    	for(int i = 0;i<n;i++){
		    		arr[i] = in.nextDouble();
		    	}
		    	
		    	
		    	Arrays.sort(arr);
		    	int f = 0;
		    	for(int i = 0;i<n;i++){
		    		temp[i] = 1-arr[i];
		    		if(temp[i] == 0.0){
		    			f = 1;
		    			break;
		    		}
		    	}
		    	
		    	if(f == 1){
		    		System.out.println(1.0);
		    		System.exit(0);
		    	}
		    	double max = 0.0;
		    	for(int i = 1;i<=n;i++){
		    		double mul = 1.0;
		    		for(int j = n-1;j>=n-i;j--){
		    			mul *= temp[j];
		    		}
		    		double ans = 0.0;
		    		for(int j = n-1;j>=n-i;j--){
		    			ans += arr[j]*(mul/temp[j]);
		    		}
		    		
		    		max = Math.max(max, ans);
		    	}
		    	
		    	System.out.println(max);
		    	
		    	//System.out.println(ans);
		//    	Segment s = new S	egment();
		//    	
		//    	s.ans();
		    	
		//    	n = in.nextInt();
		//    	arr = new int[2*n];
		//    	d = new int[n];
		//    	h = (int)Math.ceil((Math.log(n)/Math.log(2)));
		//    	for(int i = 0;i<n;i++){
		//    		arr[i+n] = in.nextInt();
		//    	}
		//    	
		//    	build();
		    	
		    	 
		   // 	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		    
		    	 
		//    	 StringBuilder sb = new StringBuilder();
		// 
		//    	 int tests = Integer.parseInt(br.readLine().trim());
		//    	  
		//          while (tests-- > 0) {
		//        	 
		//        	
		//          }
		//          
		//          
		//          System.out.println(sb.toString());
		//          
		           
		         
		}
		
		    public static void dfs(int i,double cur,int l){
		    	if(visited[i] == 1){
		    		return;
		    	}
		    	
		    	//System.out.println(i + " " + cur + " " + adj[i].size());
		    	visited[i] = 1;
		    	
		    	if(adj[i].size() == 1 && i != 0){
		    		ans += l*cur;
		    		//System.out.println(l + "ads " + cur);
		    	}else{
		    		if(i != 0)
		    		cur = cur*(1/(double)(adj[i].size()-1));
		    		else{
		    			cur = cur*(1/(double)(adj[i].size()));
		    		}
		    		for(int j = 0;j<adj[i].size();j++){
		    			
		    			dfs((int)adj[i].get(j),cur,l+1);
		    		}
		    	}
		    }
		    
		    
		    public static String[] reverse(String arr[]){
		    	
		    	
		    	for(int i = 0;i<arr.length/2;i++){
		    		String temp = arr[i];
		    		arr[i] = arr[arr.length-i-1];
		    		arr[arr.length-1-i] = temp;
		    	}
		    	
		    	return arr;
		    	
		    }
			
			
		    
		 
		    public static long sum(long x){
		    	return x<10?x:x%10 + sum(x/10);
		    }
			
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}
			private static long pow(long a, long b, long c) {
				if (b == 0)
					return 1;
				long p = pow(a, b / 2, c);
				p = (p * p) % c;
				return (b % 2 == 0) ? p : (a * p) % c;
			}
			
			
			
			
			public static boolean isPrime(int n) {
				// Corner cases
				if (n <= 1)
					return false;
				if (n <= 3)
					return true;
		 
				// This is checked so that we can skip 
				// middle five numbers in below loop
				if (n % 2 == 0 || n % 3 == 0)
					return false;
		 
				for (int i = 5; i * i <= n; i = i + 6)
					if (n % i == 0 || n % (i + 2) == 0)
						return false;
		 
				return true;
			}
			
		
			void run() throws NumberFormatException, IOException {
				in = new FastScanner();
				out = new PrintWriter(System.out);
		
				solve();
		
				out.close();
			}
		
			class FastScanner {
				BufferedReader br;
				StringTokenizer st;
		
				public FastScanner() {
					br = new BufferedReader(new InputStreamReader(System.in));
				}
		
				String next() {
					while (st == null || !st.hasMoreTokens()) {
						try {
							st = new StringTokenizer(in.br.readLine());
						} catch (IOException e) {
							// TODO Auto-generated catch block
							e.printStackTrace();
						}
					}
					return st.nextToken();
				}
		
				int nextInt() {
					return Integer.parseInt(next());
				}
		
				long nextLong() {
					return Long.parseLong(next());
				}
		
				double nextDouble() {
					return Double.parseDouble(next());
				}
			}
			
			class Tri{
				
				Tri[] arr;
				
				public Tri(){
					arr = new Tri[27];
				}
				
			}
			
			
		 
		
			public static void main(String[] args) throws NumberFormatException, IOException {
				new Main().run();
			}
		}
		
		
		class Node{
			int a;
			int b;
			
		}
		
		class MyComp implements Comparator<Node>{
		    
			@Override
			public int compare(Node a,Node b) {
				
				// < == -1
				
				if(a.a < b.a){
					return -1;
				}else if(a.a > b.a){
					return 1;
				}else{
					return 0;
				}
				
				
			}
		}