n=3 circuits=3
root 0: 2:2 3:2 4:2   [sum N = 6 = (n-1)*circ? yes ; sum i N = 18 = n(n-1)*circ? yes]
root 1: 2:2 3:2 4:2   [sum N = 6 = (n-1)*circ? yes ; sum i N = 18 = n(n-1)*circ? yes]
root 2: 2:2 3:2 4:2   [sum N = 6 = (n-1)*circ? yes ; sum i N = 18 = n(n-1)*circ? yes]
 $n  0.00s user 0.00s system 0% cpu 0.467 total
n=4 circuits=256
root 0: 2:192 3:168 4:132 5:108 6:96 7:36 8:36   [sum N = 768 = (n-1)*circ? yes ; sum i N = 3072 = n(n-1)*circ? yes]
root 1: 2:192 3:168 4:132 5:108 6:96 7:36 8:36   [sum N = 768 = (n-1)*circ? yes ; sum i N = 3072 = n(n-1)*circ? yes]
root 2: 2:192 3:168 4:132 5:108 6:96 7:36 8:36   [sum N = 768 = (n-1)*circ? yes ; sum i N = 3072 = n(n-1)*circ? yes]
root 3: 2:192 3:168 4:132 5:108 6:96 7:36 8:36   [sum N = 768 = (n-1)*circ? yes ; sum i N = 3072 = n(n-1)*circ? yes]
 $n  0.00s user 0.00s system 70% cpu 0.003 total
n=5 circuits=972000
root 0: 2:777600 3:673920 4:559872 5:467712 6:387648 7:301824 8:248832 9:166752 10:132480 11:81504 12:52992 13:18432 14:18432   [sum N = 3888000 = (n-1)*circ? yes ; sum i N = 19440000 = n(n-1)*circ? yes]
root 1: 2:777600 3:673920 4:559872 5:467712 6:387648 7:301824 8:248832 9:166752 10:132480 11:81504 12:52992 13:18432 14:18432   [sum N = 3888000 = (n-1)*circ? yes ; sum i N = 19440000 = n(n-1)*circ? yes]
root 2: 2:777600 3:673920 4:559872 5:467712 6:387648 7:301824 8:248832 9:166752 10:132480 11:81504 12:52992 13:18432 14:18432   [sum N = 3888000 = (n-1)*circ? yes ; sum i N = 19440000 = n(n-1)*circ? yes]
root 3: 2:777600 3:673920 4:559872 5:467712 6:387648 7:301824 8:248832 9:166752 10:132480 11:81504 12:52992 13:18432 14:18432   [sum N = 3888000 = (n-1)*circ? yes ; sum i N = 19440000 = n(n-1)*circ? yes]
root 4: 2:777600 3:673920 4:559872 5:467712 6:387648 7:301824 8:248832 9:166752 10:132480 11:81504 12:52992 13:18432 14:18432   [sum N = 3888000 = (n-1)*circ? yes ; sum i N = 19440000 = n(n-1)*circ? yes]
 $n  0.20s user 0.00s system 98% cpu 0.207 total
