Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
 
public class Main
{
  public static void main(String args[]) {
 Scanner sc =new Scanner(System.in);
  	int n = sc.nextInt();
  	int[]a = new int[n];
  	for(int i =0;i <a.length; i++) {
  		a[i] = sc.nextInt();
  	}
  	Arrays.sort(a);
  	int sum = 0;
  	for(int i =0; i<a.length-1; i++) {
  		sum= sum + a[i];
  		
  	}
  	if(sum<=a[a.length-1]) {
  		System.out.println("No");
  	}
  	else {
  		System.out.println("Yes");
  	}
  	
  }
  
}