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) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int le[]=new int[n];
		int max_length=0;
		int max_number=-1;
		int sum=0;
		for (int i = 0; i < n; i++) {
			le[i]=sc.nextInt();
			sum+=le[i];
			if(le[i]>max_length) {
				max_length=le[i];
				max_number=i;
			}
		}
		sum-=max_length;
		System.out.println(sum>max_length?"Yes":"No");
		
	}
}