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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, '%d', $n);
// echo $n;
// echo $m;
$max = 0;
$sum = 0;
$a = explode(' ', fgets(STDIN));
for ($j = 0; $j <= $n; $j++) {
  $sum = $sum + $a[$j];
  if ($max < $a[$j]) {
    $max = $a[$j];
  }
}

if ($max < $sum - $max) {
  echo 'Yes';
} else {
  echo 'No';
}