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 Perl (v5.18.2) (judge verdict: Wrong Answer)

use v5.18; # strict say state
use warnings;
use bignum(a=>40);

my ($a, $b, $c) = split / /, <STDIN>;

my $x = new Math::BigFloat($a)->bsqrt(2);
my $y = new Math::BigFloat($b)->bsqrt(2);
my $z = Math::BigFloat->new($c)->bsqrt(2);

if ($x+$y<$z) {
  say "Yes";
} else {
  say "No";
}