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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {
  public static void main(String[] args ) throws Exception {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    boolean M=false;
    int width[]=new int[N];
    int max=width[0];
    int sum=0;
    for(int i=0;i<N;i++){
      width[i]=sc.nextInt();
    }
    for(int i=1;i<N;i++){
      if(width[i]>max){
      	max=width[i];
      }
    }
    for(int j=0; j<N; j++){
    	sum+=width[j];
    }
    sum-=max;
    if(sum>max){
    System.out.println("Yes");
    }else{
      System.out.println("No");
    }
  }
}