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 v5.12) (judge verdict: Accepted)

'use strict'

const main = (INPUT) => {
  const input = INPUT.split('\n')
  const N = Number(input[0])
  const L = input[1].split(' ').map(n => Number(n)).sort((a, b) => b - a)
  let sum = 0
  for (let i = 1; i < N; i++) {
    sum += L[i]
  }
  if (L[0] < sum) {
    console.log('Yes')
  } else {
    console.log('No')
  }
}

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