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 {

		static void solve() {
			Scanner sc = new Scanner(System.in);
			int n = sc.nextInt();
			int sum = 0;
			String res = "No";
			int[] array = new int [n];
			for(int i = 0;i<n;i++) {
				array[i] = sc.nextInt();
				sum+=array[i];
			}
			int max = array[0];
			for(int numb:array) {
				if(numb>=max) 
					max = numb;
				}
			if(max<sum-max) {
				res = "Yes";
			}
		
			System.out.println(res);
			sc.close();
		}
	public static void main(String[] args) {
		solve();

	}

}