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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

function main(input) {
  const args = input.split('\n');
  const N = parseInt(args[0], 10);
  let ary = args[1].split(' ').map(n => parseInt(n, 10));
  let max;
  let total = 0;
  
  ary.sort((a, b) => { return b - a });
  
  for (let i = 0; i < ary.length; i++) {
    if (i === 0) { 
      max = ary[0];
    } else {
      total += ary[i];
    }
  }
  
  (max < total) ? console.log('Yes') : console.log('No');
  
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));