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 a=sc.nextInt();
		int b[]=new int [a+1];
		for(int i=0;i<a;i++)
		{
			b[i]=sc.nextInt();
			//System.out.println(b[i]);
		}
		Arrays.sort(b);
		/*for(int k=0;k<a;k++)
		{
			System.out.println(b[k]);
		}*/
		int c=0;
		for(int j=0;j<a;j++)
		{
			c=c+b[j];
			//System.out.println("c is:"+c);
		}
		if(b[a]<c)
			System.out.println("Yes");
		else
			System.out.println("No");
	}
}