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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
 
function input($func = null) {
    if ($func === null) {
        return trim(fgets(STDIN));
    } else {
        return $func(trim(fgets(STDIN)));
    }
}
function input_array($func = null) {
    if ($func === null) {
        return explode(' ', input());
    } else {
        return array_map(function($v) use ($func) {
            return $func($v);
        }, explode(' ', input()));
    }
}

$n = input('intval');
$ls = input_array('intval');
rsort($ls);

if ($ls[0] * 2 < array_sum($ls)) {
    echo "Yes\n";
} else {
    echo "No\n";
}