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.io.*;
import java.math.*;
import java.util.*;

class Main {
	public static void main(String args[]) {
    	Scanner sc = new Scanner(System.in);
      	int n = sc.nextInt();
      	//List<Integer> l = new ArrayList<Integer>();
      	int max = 0;
      	int tsum = 0;
      	while(n > 0) {
        	int ele = sc.nextInt();
          	//l.add(ele);
          	n--;
          	max = max > ele ? max : ele;
          	tsum += ele;
        }
	    System.out.println((tsum - max) > max ? "Yes" : "No");
    }
}