Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

* All values in input are integers.
* 3 \leq N \leq 10
* 1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:


N
L_1 L_2 ... L_N


Output

If an N-sided polygon satisfying the condition can be drawn, print `Yes`; otherwise, print `No`.

Examples

Input

4
3 8 5 1


Output

Yes


Input

4
3 8 4 1


Output

No


Input

10
1 8 10 5 8 12 34 100 11 3


Output

No
import java.util.*;
public class Main{
 public static void main(String[] args){
   Scanner sc = new Scanner(System.in);
   int N = sc.nextInt();
   int[] Li = new int[N];
   for(int i =0;i<N;i++) Li[i] = sc.nextInt();
   
   Arrays.sort(Li);
   int sum =0;
   for(int i =0;i<N-1;i++) sum += Li[i]; 
   
   if(Li[N-1] < sum) System.out.println("Yes");
   else System.out.println("No");
 }
}