use v6;

my @chain    = $*IN.get.comb: /\d+/;
my @matrices = @chain Z=> @chain[1..*-1];

unless +@matrices {
    say 'Input must consist of at least two integers.';
    exit;
}

my $n = 1; # should be a state var of to-string($)
my multi sub to-string(@e) { [~] '(', (to-string($_) for @e), ')' } # .map does not like me :/
my multi sub to-string($ ) { 'A' ~ $n++ }

say to-string( mul(@matrices).[1] );

# mul(*@Matrices) returns:
# 1. Cost of the multiplication.
# 2. Multiplication expression as AoA. A single matrix is represented by a 1.
# 3. Rows of the result-matrix.
# 4. Cols of the result-matrix.

my %mul; # memoization, should be a state var of mul(*@M)
sub mul(*@M) {
    my $key = @M.map( *.kv.join: 'x' ).join: '*';
    
    return  %mul{$key}                       if %mul.exists: $key;
    return (%mul{$key} = [ 0, 1, @M[0].kv ]) if +@M == 1;
    
    my ($cost, $expr, @size) = +Inf;
    
    for 0 .. @M.end - 1 -> $i {
        my ($c1, $e1, $p,   ) = @( mul @M[   0 .. $i    ] ); # lhs
        my ($c2, $e2, $q, $r) = @( mul @M[$i+1 .. @M.end] ); # rhs
        
        my $cges = $c1 + $c2 + $p*$q*$r;
        
        if $cges < $cost {
            $cost = $cges;
            $expr = [ $e1, $e2 ];
            @size = $p, $r;
        }
    }
    
    return (%mul{$key} = [ $cost, $expr, @size ]);
}