Problem:
Score : 300 points

Problem Statement

Does \sqrt{a} + \sqrt{b} < \sqrt{c} hold?

Constraints

1 \leq a, b, c \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

a \ b \ c

Output

If \sqrt{a} + \sqrt{b} < \sqrt{c}, print Yes; otherwise, print No.

Sample Input 1

2 3 9

Sample Output 1

No

\sqrt{2} + \sqrt{3} < \sqrt{9} does not hold.

Sample Input 2

2 3 10

Sample Output 2

Yes

\sqrt{2} + \sqrt{3} < \sqrt{10} holds.

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php

    list($a, $b, $c) = in_ints();

    if (add_float(sqrt($a), sqrt($b)) < sqrt($c)) {
        yes();
    } else {
        no();
    }

    function add_float($a, $b) {
        $a = strval($a);
        $b = strval($b);

        $a = explode('.', $a);
        $b = explode('.', $b);

        $left = (int)$a[0] + (int)$b[0];

        $idx = 0;
        $a_right = str_split($a[1]);
        $b_right = str_split($b[1]);
        if (count($a_right) > count($b_right)) {
            $idx = count($a_right) - 1;
        } else {
            $idx = count($b_right) - 1;
        }

        $right = [];
        $carry = false;
        while ($idx >= 0) {
            $sum = (int)@$a_right[$idx] + (int)@$b_right[$idx];
            if ($carry) {
                $sum++;
            }
            $carry = false;
            if ($sum >= 10) {
                $sum -= 10;
                $carry = true;
            }
            $right[$idx] = strval($sum);
            $idx--;
        }
        if ($carry) {
            $left++;
        }

        return (float)($left . '.' . implode('', $right));
    }
    
    /**
    * お手伝い関数さんたち
    */
    function in() {
        return trim(fgets(STDIN));
    }
    function in_int() {
        return (int)in();
    }
    function in_vals() {
        return explode(' ', in());
    }
    function in_ints() {
        return array_map('intval', in_vals());
    }
    function out($s) {
        echo $s . PHP_EOL;
    }
    function yes() {
        out('Yes');
    }
    function no() {
        out('No');
    }