Iahub and Iahubina went to a picnic in a forest full of trees. Less than 5 minutes passed before Iahub remembered of trees from programming. Moreover, he invented a new problem and Iahubina has to solve it, otherwise Iahub won't give her the food. 

Iahub asks Iahubina: can you build a rooted tree, such that

  * each internal node (a node with at least one son) has at least two sons; 
  * node i has ci nodes in its subtree? 



Iahubina has to guess the tree. Being a smart girl, she realized that it's possible no tree can follow Iahub's restrictions. In this way, Iahub will eat all the food. You need to help Iahubina: determine if there's at least one tree following Iahub's restrictions. The required tree must contain n nodes.

Input

The first line of the input contains integer n (1 ≤ n ≤ 24). Next line contains n positive integers: the i-th number represents ci (1 ≤ ci ≤ n).

Output

Output on the first line "YES" (without quotes) if there exist at least one tree following Iahub's restrictions, otherwise output "NO" (without quotes). 

Examples

Input

4
1 1 1 4


Output

YES

Input

5
1 1 5 2 1


Output

NO
import java.util.*;
import java.io.*;

public class ProblemE
{
   public static void main(String[] args)
   {
      Scanner s = new Scanner(System.in);
      
      while(s.hasNextInt())
      {
         int n = s.nextInt();
         ArrayList<Integer> internal = new ArrayList<Integer>();
         int leafNodes = 0;
         for(int i = 0; i<n; i++)
         {
            int v = s.nextInt();
            if(v==1)
               leafNodes++;
            else
               internal.add(v);
         }
         Collections.sort(internal);
         if(n==1)
         {
            System.out.println("YES");
         }
         else if(internal.size() == 0)
         {
            System.out.println("NO");
         }
         else if(internal.get(internal.size()-1)!=n)
         {
            System.out.println("NO");
         }
         else
         {
            
            leafNodes-=internal.get(0)-1;
            int minChildren = internal.get(0)-1;
            boolean[] used = new boolean[internal.size()];
            for(int i = 1; i<internal.size(); i++)
            {
               boolean found = false;
               int needed = internal.get(i)-1;
               int children = 0;
               for(int j = i-1; j>=0; j--)
               {
                  if(used[j]!=true && (internal.get(j)<needed || (internal.get(j)==needed && children!=0)))
                  {
                     needed -= internal.get(j);
                     children++;
                     used[j] = true;
                  }
               }
               if(needed>0)
               {
                  leafNodes-=needed;
                  children+=needed;
               }
               if(children<minChildren)
                  minChildren=children;
            }
         
            if(leafNodes==0 && minChildren>1)
            {
               System.out.println("YES");
            }
            else
            {
               System.out.println("NO");
            }
         }
      }
   }
}
