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.Scanner;
public class Main {

			public static void main(String[]args) {
			
				Scanner sc = new Scanner(System.in);
				int N = sc.nextInt();
				int max=0;
				int sum=0;
				int scan;
				
				for(int i =0; i<N; i++) {
					scan = sc.nextInt();
					if(scan>max) {
						sum += max;
						max = scan;
					}else {
						sum +=scan;
					}
				}
				if(max<sum)System.out.println("Yes");
				else System.out.println("No");
			}
}
