use strict;
use Algorithm::Loops qw( MapCarE NestedLoops );

my @node= ( 'a'..'e', 1..5 );

# Build regex to exclude points that don't make a triangle:
my $re= do {

    # Pairs of points that have no line between them:
    my @cant= MapCarE { join '', @_ } ['a'..'e'], [1..5];
    push @cant, map { ( $_.(($_+2)%5), $_.(($_+3)%5) ) } 1..5;
    # Make regex fragments that match when a line isn't there:
    $_= "(?:[^$_]?[$_]){2}"   for  @cant;

    # Triplets of points that are co-linear:
    my @line;
    my $x= 'a32d';
    my $y= 'a45c';
    for(  1..5  ) {
        push @line, $x, $y;
        tr/abcde12345/bcdea23451/   for  $x, $y;
    }
    # Make regex fragments that match have a line:
    $_= "[$_]{3}"   for  @line;

    "^(?:" . join( "|", @cant, @line ) . ")";
};

my $count= NestedLoops(
    [
        [ 0 .. $#node ],
        ( sub { [ $_+1 .. $#node ] } ) x 2,
    ],
    sub {
        (1) x join('',@node[@_]) !~ /$re/o;
        # if(  join('',@node[@_]) !~ /$re/o  ) {
        #     print "Yes @node[@_]\n";
        #     return 1;
        # }
        # print "No  @node[@_]\n";
        # return;
    },
);

print "$count triangles\n";