#
# optimal way to multiply a chain of matrices
# the algorithm seeks to always collapse the higher factor
# by canceling it in between the multiplications.
#

my @items = $*IN.get.comb(/\d+/);

exit say "Input must consist of at least two integers." unless @items > 1;

my @matrix = 'A' X~ 1 .. @items-1;

while @matrix > 1
{
    my $i = max { @items[$^a] > @items[$^b] }, 1 .. @items-2;
    @items.splice($i,1);
    @matrix.splice($i-1,2,'('~@matrix[$i-1]~@matrix[$i]~')');
}

say @matrix[0];