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[] data = new int[n];
      int sum = 0;
      int max = 0;
      for (int i = 0;i<n ;i++ ) {
        data[i] = sc.nextInt();
        max = Math.max(max,data[i]);
        sum += data[i];
      }
      if(sum-max>max){
        System.out.println("Yes");
      }else{
        System.out.println("No");
      }
      
}
}
