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[]a = new int[n];
  	for(int i =0;i <a.length; i++) {
  		a[i] = sc.nextInt();
  	}
  	Arrays.sort(a);
  	int sum = 0;
  	for(int i =0; i<a.length-1; i++) {
  		sum= sum + a[i];
  		
  	}
  	if(sum<=a[a.length-1]) {
  		System.out.println("No");
  	}
  	else {
  		System.out.println("Yes");
  	}
  	
  }
  
}