#! perl -slw
use strict;
use overload;
use Math::Big::Factors qw[ factors_wheel ];
use List::Util qw[ reduce min ];
use Algorithm::Loops qw[ NestedLoops ];

my $NUM = $ARGV[ 0 ] || 996;

my $root = sqrt $NUM;
my @pfs = reverse map{ "$_" } factors_wheel( $NUM );

print "$NUM primefactors ( @pfs )";

my $n = 0;

while( $root <= reduce{ $a * $b } @pfs ) {
	my $near = reduce{ 
		( $a * $b ) <= $root ? $a*$b : 0+$a
	}  @pfs;
	$n = $near 
		if abs( $root - $near ) < abs( $root - $n );
	$n = $near * $pfs[ -1 ] 
		if abs( $root - $n ) > ( $near * $pfs[ -1 ] - $root );
	my $discard = shift @pfs;
	next if $pfs[ 0 ] == $discard;
	unshift @pfs, $pfs[0] while $root > reduce{ $a * $b } @pfs;
}

print "$NUM ($root} : $n";

__END__
P:\test>432558
996 primefactors ( 83 3 2 2 )
996 (31.559467676119} : 36

P:\test>432558 1000
1000 primefactors ( 5 5 5 2 2 2 )
1000 (31.6227766016838} : 32

P:\test>432558  100000000000000
100000000000000 primefactors ( 5 5 5 5 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 )
100000000000000 (10000000} : 10000000

P:\test>432558  10000000000000
10000000000000 primefactors ( 5 5 5 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 2 2 2 )
10000000000000 (3162277.66016838} : 3125000

P:\test>432558  1995
1995 primefactors ( 19 7 5 3 )
1995 (44.6654228682546} : 35