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: Wrong Answer)

<?php

fscanf(STDIN, '%d', $N);
$line = array_map('intVal', explode(' ', trim(fgets(STDIN))));

sort($line);

for ($i = 1; $i <= $N-1; ++$i) {
    $other_sum = $line[$i];
}

if ($line[0] < $other_sum) {
    $diff = $other_sum - $line[0];
    if (in_array($diff, $line)) {
        echo 'Yes';
    } else {
        echo 'No';
    }
} else {
    echo 'No';
}