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srand(1);  # So everything is using the same numbers
my $s = 0;
for (1..1000000) {
  $s += nearest_sqrt(int(rand(2**47)));
}
print "$s\n";

use ntheory qw/divisors/;
sub closest {
  my @d = divisors(shift);
  $d[ $#d >> 1 ];
}

use ntheory qw/fordivisors/;
sub closest {
  my($n,$sqrtn,$min) = ($_[0], int(sqrt($_[0])));
  fordivisors { $min = $_ if $_ <= $sqrtn; } $n;
  $min;
}

use ntheory qw/factor/;
sub closest {
  my($n) = @_;
...
  # 4. Return the largest divisor <= sqrt n.
  $d[ $#d >> 1 ];
}

use Math::Pari qw/divisors/;
sub closest {
  my $d = divisors(shift);
  $d->[ $#$d >> 1 ];
}

use Math::Factor::XS qw/factors/;
sub closest {
  my @d = (1, factors($_[0]), $_[0]);
  $d[ $#d >> 1 ];
}