ok    Lemma 2.2: the tuple (z,a,b,p,c,q,r,x) uses za, zb, zc and 9 pairs inside K (|K| = 7 used)
ok    Lemma 2.5: the two tuples certify s0s3 and then s0z
ok    Lemma 2.5: the face gadget on K_7 percolates (closure computed)
ok    Lemma 2.5: the face gadget on K_8 percolates (closure computed)
ok    Lemma 2.2: K_7 plus a vertex with two neighbours percolates
ok    Lemma 4.1: ex(2..7) = 1,2,4,5,7,9 (all subsets of Q_3)
ok    Remark 4.2: e_1..e_7 = 2,4,6,7,9,10,11
ok    Remark 4.2: e_i = 11 - ex(8 - i)
ok    Remark 4.2: min_{i<=7} e_i/i = 11/7, min_{i<=6} e_i/i = 5/3
ok    Remark 4.2: g*_2(1) + 11 = e_1 + 11 = 13 < 16
ok    (2): f(8)=11, f(2)=1, 11-8a+c=0, 2a-c=1
ok    (2): slacks a*w-c-ex(w) = 0,2/3,1/3,1,2/3,1/3
ok    Remark 4.2: the scheme allows slope at most (11-ex(2))/6 = 5/3
ok    end game: a - c/8 = 11/8, a - c/2 = 1/2
ok    end game: min over n = 8..80 of the weight w(x) is 15/8
ok    Table 1: ceil((5n-7)/3) for n = 8..18
ok    Table 1: floor((7n+2)/4) for n = 8..18
ok    Theorem 1.3: floor((7(n+4)+2)/4) = floor((7n+2)/4) + 7
ok    Theorem 1.2 agrees with floor((7n+2)/4) for 9 <= n <= 13
ok    Theorem 1.2 is consistent with Theorem 1.4
ok    Proposition 5.1: k = 3,4,6,7,9,11 give the lower bounds 12 + k = 15,16,18,19,21,23
ok    upper bounds: 16+2, 19+2, 16+7
ok    Table 2: S_8 has 15 edges
ok    Table 3: certificates of S_8 as printed: 11 listed steps, complete set [0, 1, 2, 3, 4, 5, 7], then [6] absorbed
ok    S_8: the full closure (computed independently of Table 3) is K_8
ok    Table 2: S_9 has 16 edges
ok    Table 3: certificates of S_9 as printed: 12 listed steps, complete set [0, 1, 2, 3, 4, 5, 7], then [6, 8] absorbed
ok    S_9: the full closure (computed independently of Table 3) is K_9
ok    Table 2: S_11 has 19 edges
ok    Table 3: certificates of S_11 as printed: 15 listed steps, complete set [0, 1, 2, 3, 4, 6, 7], then [5, 8, 9, 10] absorbed
ok    S_11: the full closure (computed independently of Table 3) is K_11
ok    S_9 restricted to {0..7}: 14 edges, closure not complete
ok    Corollary 2.3 instance: S_9 plus a vertex joined to 0, 1 percolates (18 edges)
ok    Corollary 2.3 instance: S_11 plus a vertex joined to 0, 1 percolates (21 edges)
ok    other seed for n = 10 (18 edges) percolates
ok    other seed for n = 12 (21 edges) percolates
ok    Section 3: the explicit graph for n = 13 (23 edges) percolates
composite n=13: S_9 + 1 gadget(s) at 0,1,2,3; 23 edges; 55 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 0, 4, 5]
    add 7-8  certificate [7, 3, 5, 0, 8, 2, 4, 1]
    add 9-12  certificate [9, 0, 11, 2, 12, 3, 10, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 8]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 8, 4]
    add 1-8  certificate [1, 0, 3, 2, 8, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 8, 4]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-9  certificate [4, 2, 3, 1, 9, 11, 12, 10]
    add 4-10  certificate [4, 2, 3, 0, 10, 11, 12, 9]
    add 4-11  certificate [4, 0, 1, 3, 11, 9, 10, 12]
    add 4-12  certificate [4, 0, 1, 2, 12, 9, 10, 11]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 2, 1, 9, 4, 11, 10]
    add 5-10  certificate [5, 0, 2, 3, 10, 1, 4, 6]
    add 5-11  certificate [5, 0, 1, 2, 11, 9, 10, 4]
    add 5-12  certificate [5, 0, 1, 2, 12, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 4, 5, 3]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 3, 4, 5]
    add 7-9  certificate [7, 1, 2, 0, 9, 4, 5, 3]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 4, 5, 3]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 3, 4, 5]
    add 9-10  certificate [9, 0, 4, 1, 10, 5, 6, 2]
    add 11-12  certificate [11, 2, 4, 0, 12, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
composite n=14: S_10 + 1 gadget(s) at 0,1,2,3; 25 edges; 66 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 4-9  certificate [4, 5, 6, 7, 9, 0, 2, 3]
    add 7-9  certificate [7, 3, 5, 0, 9, 2, 4, 1]
    add 10-13  certificate [10, 0, 12, 2, 13, 3, 11, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 9]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 9]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 9, 4]
    add 1-9  certificate [1, 0, 3, 2, 9, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 9, 4]
    add 2-8  certificate [2, 3, 5, 7, 8, 0, 1, 6]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 4, 5, 8, 1, 2, 7]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-10  certificate [4, 2, 3, 1, 10, 12, 13, 11]
    add 4-11  certificate [4, 2, 3, 0, 11, 12, 13, 10]
    add 4-12  certificate [4, 0, 1, 3, 12, 10, 11, 13]
    add 4-13  certificate [4, 0, 1, 2, 13, 10, 11, 12]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 5-10  certificate [5, 0, 2, 1, 10, 4, 12, 11]
    add 5-11  certificate [5, 0, 2, 3, 11, 1, 4, 6]
    add 5-12  certificate [5, 0, 1, 2, 12, 10, 11, 4]
    add 5-13  certificate [5, 0, 1, 2, 13, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 3, 4, 5]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 3, 4, 5]
    add 7-8  certificate [7, 1, 2, 0, 8, 3, 4, 5]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 4, 5, 3]
    add 7-13  certificate [7, 1, 2, 0, 13, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 3, 4, 5]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 3, 4, 5]
    add 9-10  certificate [9, 0, 1, 2, 10, 4, 5, 3]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 3, 4, 5]
    add 10-11  certificate [10, 0, 4, 1, 11, 5, 6, 2]
    add 12-13  certificate [12, 2, 4, 0, 13, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
composite n=15: S_11 + 1 gadget(s) at 0,1,2,3; 26 edges; 79 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 8-10  certificate [8, 1, 9, 3, 10, 5, 2, 0]
    add 2-7  certificate [2, 9, 10, 8, 7, 3, 5, 1]
    add 7-8  certificate [7, 2, 3, 0, 8, 10, 1, 5]
    add 0-8  certificate [0, 2, 3, 7, 8, 10, 1, 5]
    add 1-2  certificate [1, 3, 5, 0, 2, 7, 10, 8]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 0, 6, 4, 8, 1, 7, 5]
    add 3-4  certificate [3, 0, 2, 8, 4, 5, 6, 7]
    add 3-5  certificate [3, 2, 4, 0, 5, 7, 1, 8]
    add 3-6  certificate [3, 0, 2, 1, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 5, 4, 8, 2, 7, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 5, 8, 7]
    add 4-7  certificate [4, 0, 1, 2, 7, 3, 5, 10]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-9  certificate [4, 0, 1, 2, 9, 3, 8, 7]
    add 4-10  certificate [4, 0, 1, 2, 10, 3, 5, 7]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 6-8  certificate [6, 2, 3, 0, 8, 1, 4, 5]
    add 6-9  certificate [6, 2, 3, 0, 9, 8, 4, 1]
    add 6-10  certificate [6, 2, 3, 0, 10, 8, 4, 1]
    add 7-9  certificate [7, 2, 3, 0, 9, 6, 4, 5]
    add 7-10  certificate [7, 2, 3, 0, 10, 6, 4, 5]
    add 9-10  certificate [9, 2, 3, 0, 10, 6, 4, 5]
    add 11-14  certificate [11, 0, 13, 2, 14, 3, 12, 1]
    add 0-6  certificate [0, 1, 2, 3, 6, 4, 7, 5]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 6, 5]
    add 0-9  certificate [0, 1, 2, 3, 9, 4, 6, 5]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 6, 5]
    add 1-6  certificate [1, 0, 2, 3, 6, 4, 7, 5]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 6, 5]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 6, 5]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 6, 5]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 1, 3, 5, 4, 6, 7]
    add 4-11  certificate [4, 2, 3, 1, 11, 13, 14, 12]
    add 4-12  certificate [4, 2, 3, 0, 12, 13, 14, 11]
    add 4-13  certificate [4, 0, 1, 3, 13, 11, 12, 14]
    add 4-14  certificate [4, 0, 1, 2, 14, 11, 12, 13]
    add 5-11  certificate [5, 0, 2, 1, 11, 4, 13, 12]
    add 5-12  certificate [5, 0, 2, 3, 12, 1, 4, 6]
    add 5-13  certificate [5, 0, 1, 2, 13, 11, 12, 4]
    add 5-14  certificate [5, 0, 1, 2, 14, 3, 4, 6]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 3, 4, 5]
    add 7-11  certificate [7, 0, 1, 2, 11, 4, 5, 3]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 3, 4, 5]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 3, 4, 5]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 3, 4, 5]
    add 10-11  certificate [10, 0, 1, 2, 11, 4, 5, 3]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 3, 4, 5]
    add 11-12  certificate [11, 0, 4, 1, 12, 5, 6, 2]
    add 13-14  certificate [13, 2, 4, 0, 14, 3, 5, 1]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
composite n=16: S_12 + 1 gadget(s) at 0,1,2,3; 28 edges; 92 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 1, 4, 5]
    add 7-8  certificate [7, 3, 5, 1, 8, 2, 4, 0]
    add 0-7  certificate [0, 1, 2, 8, 7, 5, 6, 4]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 2-4  certificate [2, 0, 6, 7, 4, 10, 9, 11]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 3-4  certificate [3, 1, 2, 0, 4, 5, 6, 7]
    add 3-6  certificate [3, 2, 7, 0, 6, 4, 11, 10]
    add 3-9  certificate [3, 2, 7, 0, 9, 4, 11, 10]
    add 3-10  certificate [3, 1, 9, 6, 10, 0, 4, 2]
    add 3-11  certificate [3, 4, 6, 2, 11, 10, 7, 0]
    add 4-7  certificate [4, 2, 6, 3, 7, 0, 11, 10]
    add 4-11  certificate [4, 0, 3, 1, 11, 7, 9, 6]
    add 5-6  certificate [5, 1, 2, 0, 6, 3, 4, 7]
    add 5-8  certificate [5, 2, 6, 3, 8, 4, 7, 11]
    add 5-9  certificate [5, 1, 2, 0, 9, 3, 4, 7]
    add 5-10  certificate [5, 1, 2, 0, 10, 3, 4, 7]
    add 5-11  certificate [5, 1, 2, 0, 11, 3, 4, 7]
    add 6-8  certificate [6, 1, 2, 0, 8, 5, 4, 7]
    add 6-10  certificate [6, 1, 2, 0, 10, 3, 4, 7]
    add 7-9  certificate [7, 0, 3, 1, 9, 4, 6, 5]
    add 7-10  certificate [7, 0, 3, 1, 10, 4, 6, 5]
    add 8-9  certificate [8, 1, 2, 0, 9, 3, 4, 7]
    add 8-10  certificate [8, 1, 2, 0, 10, 3, 4, 7]
    add 8-11  certificate [8, 1, 2, 0, 11, 3, 4, 7]
    add 9-10  certificate [9, 3, 4, 2, 10, 6, 5, 8]
    add 0-3  certificate [0, 1, 2, 5, 3, 6, 4, 7]
    add 0-5  certificate [0, 1, 2, 3, 5, 6, 4, 7]
    add 0-6  certificate [0, 1, 2, 3, 6, 5, 4, 7]
    add 0-8  certificate [0, 1, 2, 3, 8, 5, 4, 6]
    add 0-9  certificate [0, 1, 2, 3, 9, 5, 4, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 5, 4, 6]
    add 1-2  certificate [1, 0, 3, 4, 2, 5, 6, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 2-7  certificate [2, 0, 1, 3, 7, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 6, 7]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 5, 6]
    add 12-15  certificate [12, 0, 14, 2, 15, 3, 13, 1]
    add 4-12  certificate [4, 2, 3, 1, 12, 14, 15, 13]
    add 4-13  certificate [4, 2, 3, 0, 13, 14, 15, 12]
    add 4-14  certificate [4, 0, 1, 3, 14, 12, 13, 15]
    add 4-15  certificate [4, 0, 1, 2, 15, 12, 13, 14]
    add 5-12  certificate [5, 0, 2, 1, 12, 4, 14, 13]
    add 5-13  certificate [5, 0, 2, 3, 13, 1, 4, 6]
    add 5-14  certificate [5, 0, 1, 2, 14, 12, 13, 4]
    add 5-15  certificate [5, 0, 1, 2, 15, 3, 4, 6]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 3, 4, 5]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 4, 5, 3]
    add 7-15  certificate [7, 0, 1, 2, 15, 3, 4, 5]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 3, 4, 5]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 4, 5, 3]
    add 9-15  certificate [9, 0, 1, 2, 15, 3, 4, 5]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 4, 5, 3]
    add 10-15  certificate [10, 0, 1, 2, 15, 3, 4, 5]
    add 11-12  certificate [11, 0, 1, 2, 12, 4, 5, 3]
    add 11-13  certificate [11, 0, 1, 2, 13, 4, 5, 3]
    add 11-14  certificate [11, 0, 1, 2, 14, 4, 5, 3]
    add 11-15  certificate [11, 0, 1, 2, 15, 3, 4, 5]
    add 12-13  certificate [12, 0, 4, 1, 13, 5, 6, 2]
    add 14-15  certificate [14, 2, 4, 0, 15, 3, 5, 1]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
composite n=17: S_9 + 2 gadget(s) at 0,1,2,3; 30 edges; 106 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 0, 4, 5]
    add 7-8  certificate [7, 3, 5, 0, 8, 2, 4, 1]
    add 9-12  certificate [9, 0, 11, 2, 12, 3, 10, 1]
    add 13-16  certificate [13, 0, 15, 2, 16, 3, 14, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 8]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 8, 4]
    add 1-8  certificate [1, 0, 3, 2, 8, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 8, 4]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-9  certificate [4, 2, 3, 1, 9, 11, 12, 10]
    add 4-10  certificate [4, 2, 3, 0, 10, 11, 12, 9]
    add 4-11  certificate [4, 0, 1, 3, 11, 9, 10, 12]
    add 4-12  certificate [4, 0, 1, 2, 12, 9, 10, 11]
    add 4-13  certificate [4, 2, 3, 1, 13, 15, 16, 14]
    add 4-14  certificate [4, 2, 3, 0, 14, 15, 16, 13]
    add 4-15  certificate [4, 0, 1, 3, 15, 13, 14, 16]
    add 4-16  certificate [4, 0, 1, 2, 16, 13, 14, 15]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 2, 1, 9, 4, 11, 10]
    add 5-10  certificate [5, 0, 2, 3, 10, 1, 4, 6]
    add 5-11  certificate [5, 0, 1, 2, 11, 9, 10, 4]
    add 5-12  certificate [5, 0, 1, 2, 12, 3, 4, 6]
    add 5-13  certificate [5, 0, 2, 1, 13, 4, 15, 14]
    add 5-14  certificate [5, 0, 2, 3, 14, 1, 4, 6]
    add 5-15  certificate [5, 0, 1, 2, 15, 13, 14, 4]
    add 5-16  certificate [5, 0, 1, 2, 16, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 4, 5, 3]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 3, 4, 5]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 3, 4, 5]
    add 7-9  certificate [7, 1, 2, 0, 9, 4, 5, 3]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 3, 4, 5]
    add 7-13  certificate [7, 1, 2, 0, 13, 4, 5, 3]
    add 7-14  certificate [7, 1, 2, 0, 14, 4, 5, 3]
    add 7-15  certificate [7, 1, 2, 0, 15, 4, 5, 3]
    add 7-16  certificate [7, 1, 2, 0, 16, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 4, 5, 3]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 3, 4, 5]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 3, 4, 5]
    add 9-10  certificate [9, 0, 4, 1, 10, 5, 6, 2]
    add 9-13  certificate [9, 0, 4, 1, 13, 5, 6, 2]
    add 9-14  certificate [9, 0, 4, 1, 14, 5, 6, 2]
    add 9-15  certificate [9, 0, 4, 1, 15, 2, 5, 3]
    add 9-16  certificate [9, 0, 4, 1, 16, 3, 5, 2]
    add 10-13  certificate [10, 1, 4, 0, 13, 5, 6, 2]
    add 10-14  certificate [10, 1, 4, 0, 14, 5, 6, 2]
    add 10-15  certificate [10, 1, 4, 0, 15, 2, 5, 3]
    add 10-16  certificate [10, 1, 4, 0, 16, 3, 5, 2]
    add 11-12  certificate [11, 2, 4, 0, 12, 3, 5, 1]
    add 11-13  certificate [11, 2, 4, 0, 13, 5, 6, 1]
    add 11-14  certificate [11, 2, 4, 0, 14, 1, 5, 3]
    add 11-15  certificate [11, 2, 4, 0, 15, 5, 6, 1]
    add 11-16  certificate [11, 2, 4, 0, 16, 3, 5, 1]
    add 12-13  certificate [12, 3, 4, 0, 13, 5, 6, 1]
    add 12-14  certificate [12, 3, 4, 0, 14, 1, 5, 2]
    add 12-15  certificate [12, 3, 4, 0, 15, 2, 5, 1]
    add 12-16  certificate [12, 3, 4, 0, 16, 5, 6, 1]
    add 13-14  certificate [13, 0, 4, 1, 14, 5, 6, 2]
    add 15-16  certificate [15, 2, 4, 0, 16, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
composite n=18: S_10 + 2 gadget(s) at 0,1,2,3; 32 edges; 121 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 4-9  certificate [4, 5, 6, 7, 9, 0, 2, 3]
    add 7-9  certificate [7, 3, 5, 0, 9, 2, 4, 1]
    add 10-13  certificate [10, 0, 12, 2, 13, 3, 11, 1]
    add 14-17  certificate [14, 0, 16, 2, 17, 3, 15, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 9]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 9]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 9, 4]
    add 1-9  certificate [1, 0, 3, 2, 9, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 9, 4]
    add 2-8  certificate [2, 3, 5, 7, 8, 0, 1, 6]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 4, 5, 8, 1, 2, 7]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-10  certificate [4, 2, 3, 1, 10, 12, 13, 11]
    add 4-11  certificate [4, 2, 3, 0, 11, 12, 13, 10]
    add 4-12  certificate [4, 0, 1, 3, 12, 10, 11, 13]
    add 4-13  certificate [4, 0, 1, 2, 13, 10, 11, 12]
    add 4-14  certificate [4, 2, 3, 1, 14, 16, 17, 15]
    add 4-15  certificate [4, 2, 3, 0, 15, 16, 17, 14]
    add 4-16  certificate [4, 0, 1, 3, 16, 14, 15, 17]
    add 4-17  certificate [4, 0, 1, 2, 17, 14, 15, 16]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 5-10  certificate [5, 0, 2, 1, 10, 4, 12, 11]
    add 5-11  certificate [5, 0, 2, 3, 11, 1, 4, 6]
    add 5-12  certificate [5, 0, 1, 2, 12, 10, 11, 4]
    add 5-13  certificate [5, 0, 1, 2, 13, 3, 4, 6]
    add 5-14  certificate [5, 0, 2, 1, 14, 4, 16, 15]
    add 5-15  certificate [5, 0, 2, 3, 15, 1, 4, 6]
    add 5-16  certificate [5, 0, 1, 2, 16, 14, 15, 4]
    add 5-17  certificate [5, 0, 1, 2, 17, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 3, 4, 5]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 3, 4, 5]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 3, 4, 5]
    add 7-8  certificate [7, 1, 2, 0, 8, 3, 4, 5]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 4, 5, 3]
    add 7-13  certificate [7, 1, 2, 0, 13, 3, 4, 5]
    add 7-14  certificate [7, 1, 2, 0, 14, 4, 5, 3]
    add 7-15  certificate [7, 1, 2, 0, 15, 4, 5, 3]
    add 7-16  certificate [7, 1, 2, 0, 16, 4, 5, 3]
    add 7-17  certificate [7, 1, 2, 0, 17, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 3, 4, 5]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 3, 4, 5]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 3, 4, 5]
    add 9-10  certificate [9, 0, 1, 2, 10, 4, 5, 3]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 3, 4, 5]
    add 9-14  certificate [9, 0, 1, 2, 14, 4, 5, 3]
    add 9-15  certificate [9, 0, 1, 2, 15, 4, 5, 3]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 3, 4, 5]
    add 10-11  certificate [10, 0, 4, 1, 11, 5, 6, 2]
    add 10-14  certificate [10, 0, 4, 1, 14, 5, 6, 2]
    add 10-15  certificate [10, 0, 4, 1, 15, 5, 6, 2]
    add 10-16  certificate [10, 0, 4, 1, 16, 2, 5, 3]
    add 10-17  certificate [10, 0, 4, 1, 17, 3, 5, 2]
    add 11-14  certificate [11, 1, 4, 0, 14, 5, 6, 2]
    add 11-15  certificate [11, 1, 4, 0, 15, 5, 6, 2]
    add 11-16  certificate [11, 1, 4, 0, 16, 2, 5, 3]
    add 11-17  certificate [11, 1, 4, 0, 17, 3, 5, 2]
    add 12-13  certificate [12, 2, 4, 0, 13, 3, 5, 1]
    add 12-14  certificate [12, 2, 4, 0, 14, 5, 6, 1]
    add 12-15  certificate [12, 2, 4, 0, 15, 1, 5, 3]
    add 12-16  certificate [12, 2, 4, 0, 16, 5, 6, 1]
    add 12-17  certificate [12, 2, 4, 0, 17, 3, 5, 1]
    add 13-14  certificate [13, 3, 4, 0, 14, 5, 6, 1]
    add 13-15  certificate [13, 3, 4, 0, 15, 1, 5, 2]
    add 13-16  certificate [13, 3, 4, 0, 16, 2, 5, 1]
    add 13-17  certificate [13, 3, 4, 0, 17, 5, 6, 1]
    add 14-15  certificate [14, 0, 4, 1, 15, 5, 6, 2]
    add 16-17  certificate [16, 2, 4, 0, 17, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 1-17  certificate [1, 0, 2, 3, 17, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-17  certificate [2, 0, 1, 3, 17, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
composite n=19: S_11 + 2 gadget(s) at 0,1,2,3; 33 edges; 138 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 8-10  certificate [8, 1, 9, 3, 10, 5, 2, 0]
    add 2-7  certificate [2, 9, 10, 8, 7, 3, 5, 1]
    add 7-8  certificate [7, 2, 3, 0, 8, 10, 1, 5]
    add 0-8  certificate [0, 2, 3, 7, 8, 10, 1, 5]
    add 1-2  certificate [1, 3, 5, 0, 2, 7, 10, 8]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 0, 6, 4, 8, 1, 7, 5]
    add 3-4  certificate [3, 0, 2, 8, 4, 5, 6, 7]
    add 3-5  certificate [3, 2, 4, 0, 5, 7, 1, 8]
    add 3-6  certificate [3, 0, 2, 1, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 5, 4, 8, 2, 7, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 5, 8, 7]
    add 4-7  certificate [4, 0, 1, 2, 7, 3, 5, 10]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-9  certificate [4, 0, 1, 2, 9, 3, 8, 7]
    add 4-10  certificate [4, 0, 1, 2, 10, 3, 5, 7]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 6-8  certificate [6, 2, 3, 0, 8, 1, 4, 5]
    add 6-9  certificate [6, 2, 3, 0, 9, 8, 4, 1]
    add 6-10  certificate [6, 2, 3, 0, 10, 8, 4, 1]
    add 7-9  certificate [7, 2, 3, 0, 9, 6, 4, 5]
    add 7-10  certificate [7, 2, 3, 0, 10, 6, 4, 5]
    add 9-10  certificate [9, 2, 3, 0, 10, 6, 4, 5]
    add 11-14  certificate [11, 0, 13, 2, 14, 3, 12, 1]
    add 15-18  certificate [15, 0, 17, 2, 18, 3, 16, 1]
    add 0-6  certificate [0, 1, 2, 3, 6, 4, 7, 5]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 6, 5]
    add 0-9  certificate [0, 1, 2, 3, 9, 4, 6, 5]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 6, 5]
    add 1-6  certificate [1, 0, 2, 3, 6, 4, 7, 5]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 6, 5]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 6, 5]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 6, 5]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 1, 3, 5, 4, 6, 7]
    add 4-11  certificate [4, 2, 3, 1, 11, 13, 14, 12]
    add 4-12  certificate [4, 2, 3, 0, 12, 13, 14, 11]
    add 4-13  certificate [4, 0, 1, 3, 13, 11, 12, 14]
    add 4-14  certificate [4, 0, 1, 2, 14, 11, 12, 13]
    add 4-15  certificate [4, 2, 3, 1, 15, 17, 18, 16]
    add 4-16  certificate [4, 2, 3, 0, 16, 17, 18, 15]
    add 4-17  certificate [4, 0, 1, 3, 17, 15, 16, 18]
    add 4-18  certificate [4, 0, 1, 2, 18, 15, 16, 17]
    add 5-11  certificate [5, 0, 2, 1, 11, 4, 13, 12]
    add 5-12  certificate [5, 0, 2, 3, 12, 1, 4, 6]
    add 5-13  certificate [5, 0, 1, 2, 13, 11, 12, 4]
    add 5-14  certificate [5, 0, 1, 2, 14, 3, 4, 6]
    add 5-15  certificate [5, 0, 2, 1, 15, 4, 17, 16]
    add 5-16  certificate [5, 0, 2, 3, 16, 1, 4, 6]
    add 5-17  certificate [5, 0, 1, 2, 17, 15, 16, 4]
    add 5-18  certificate [5, 0, 1, 2, 18, 3, 4, 6]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 3, 4, 5]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 4, 5, 3]
    add 6-18  certificate [6, 0, 1, 2, 18, 3, 4, 5]
    add 7-11  certificate [7, 0, 1, 2, 11, 4, 5, 3]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 3, 4, 5]
    add 7-15  certificate [7, 0, 1, 2, 15, 4, 5, 3]
    add 7-16  certificate [7, 0, 1, 2, 16, 4, 5, 3]
    add 7-17  certificate [7, 0, 1, 2, 17, 4, 5, 3]
    add 7-18  certificate [7, 0, 1, 2, 18, 3, 4, 5]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 3, 4, 5]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 4, 5, 3]
    add 8-18  certificate [8, 0, 1, 2, 18, 3, 4, 5]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 3, 4, 5]
    add 9-15  certificate [9, 0, 1, 2, 15, 4, 5, 3]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 4, 5, 3]
    add 9-18  certificate [9, 0, 1, 2, 18, 3, 4, 5]
    add 10-11  certificate [10, 0, 1, 2, 11, 4, 5, 3]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 3, 4, 5]
    add 10-15  certificate [10, 0, 1, 2, 15, 4, 5, 3]
    add 10-16  certificate [10, 0, 1, 2, 16, 4, 5, 3]
    add 10-17  certificate [10, 0, 1, 2, 17, 4, 5, 3]
    add 10-18  certificate [10, 0, 1, 2, 18, 3, 4, 5]
    add 11-12  certificate [11, 0, 4, 1, 12, 5, 6, 2]
    add 11-15  certificate [11, 0, 4, 1, 15, 5, 6, 2]
    add 11-16  certificate [11, 0, 4, 1, 16, 5, 6, 2]
    add 11-17  certificate [11, 0, 4, 1, 17, 2, 5, 3]
    add 11-18  certificate [11, 0, 4, 1, 18, 3, 5, 2]
    add 12-15  certificate [12, 1, 4, 0, 15, 5, 6, 2]
    add 12-16  certificate [12, 1, 4, 0, 16, 5, 6, 2]
    add 12-17  certificate [12, 1, 4, 0, 17, 2, 5, 3]
    add 12-18  certificate [12, 1, 4, 0, 18, 3, 5, 2]
    add 13-14  certificate [13, 2, 4, 0, 14, 3, 5, 1]
    add 13-15  certificate [13, 2, 4, 0, 15, 5, 6, 1]
    add 13-16  certificate [13, 2, 4, 0, 16, 1, 5, 3]
    add 13-17  certificate [13, 2, 4, 0, 17, 5, 6, 1]
    add 13-18  certificate [13, 2, 4, 0, 18, 3, 5, 1]
    add 14-15  certificate [14, 3, 4, 0, 15, 5, 6, 1]
    add 14-16  certificate [14, 3, 4, 0, 16, 1, 5, 2]
    add 14-17  certificate [14, 3, 4, 0, 17, 2, 5, 1]
    add 14-18  certificate [14, 3, 4, 0, 18, 5, 6, 1]
    add 15-16  certificate [15, 0, 4, 1, 16, 5, 6, 2]
    add 17-18  certificate [17, 2, 4, 0, 18, 3, 5, 1]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 0-18  certificate [0, 1, 2, 3, 18, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-17  certificate [1, 0, 2, 3, 17, 4, 5, 6]
    add 1-18  certificate [1, 0, 2, 3, 18, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 2-18  certificate [2, 0, 1, 3, 18, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
    add 3-17  certificate [3, 0, 1, 2, 17, 4, 5, 6]
composite n=20: S_12 + 2 gadget(s) at 0,1,2,3; 35 edges; 155 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 1, 4, 5]
    add 7-8  certificate [7, 3, 5, 1, 8, 2, 4, 0]
    add 0-7  certificate [0, 1, 2, 8, 7, 5, 6, 4]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 2-4  certificate [2, 0, 6, 7, 4, 10, 9, 11]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 3-4  certificate [3, 1, 2, 0, 4, 5, 6, 7]
    add 3-6  certificate [3, 2, 7, 0, 6, 4, 11, 10]
    add 3-9  certificate [3, 2, 7, 0, 9, 4, 11, 10]
    add 3-10  certificate [3, 1, 9, 6, 10, 0, 4, 2]
    add 3-11  certificate [3, 4, 6, 2, 11, 10, 7, 0]
    add 4-7  certificate [4, 2, 6, 3, 7, 0, 11, 10]
    add 4-11  certificate [4, 0, 3, 1, 11, 7, 9, 6]
    add 5-6  certificate [5, 1, 2, 0, 6, 3, 4, 7]
    add 5-8  certificate [5, 2, 6, 3, 8, 4, 7, 11]
    add 5-9  certificate [5, 1, 2, 0, 9, 3, 4, 7]
    add 5-10  certificate [5, 1, 2, 0, 10, 3, 4, 7]
    add 5-11  certificate [5, 1, 2, 0, 11, 3, 4, 7]
    add 6-8  certificate [6, 1, 2, 0, 8, 5, 4, 7]
    add 6-10  certificate [6, 1, 2, 0, 10, 3, 4, 7]
    add 7-9  certificate [7, 0, 3, 1, 9, 4, 6, 5]
    add 7-10  certificate [7, 0, 3, 1, 10, 4, 6, 5]
    add 8-9  certificate [8, 1, 2, 0, 9, 3, 4, 7]
    add 8-10  certificate [8, 1, 2, 0, 10, 3, 4, 7]
    add 8-11  certificate [8, 1, 2, 0, 11, 3, 4, 7]
    add 9-10  certificate [9, 3, 4, 2, 10, 6, 5, 8]
    add 0-3  certificate [0, 1, 2, 5, 3, 6, 4, 7]
    add 0-5  certificate [0, 1, 2, 3, 5, 6, 4, 7]
    add 0-6  certificate [0, 1, 2, 3, 6, 5, 4, 7]
    add 0-8  certificate [0, 1, 2, 3, 8, 5, 4, 6]
    add 0-9  certificate [0, 1, 2, 3, 9, 5, 4, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 5, 4, 6]
    add 1-2  certificate [1, 0, 3, 4, 2, 5, 6, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 2-7  certificate [2, 0, 1, 3, 7, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 6, 7]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 5, 6]
    add 12-15  certificate [12, 0, 14, 2, 15, 3, 13, 1]
    add 16-19  certificate [16, 0, 18, 2, 19, 3, 17, 1]
    add 4-12  certificate [4, 2, 3, 1, 12, 14, 15, 13]
    add 4-13  certificate [4, 2, 3, 0, 13, 14, 15, 12]
    add 4-14  certificate [4, 0, 1, 3, 14, 12, 13, 15]
    add 4-15  certificate [4, 0, 1, 2, 15, 12, 13, 14]
    add 4-16  certificate [4, 2, 3, 1, 16, 18, 19, 17]
    add 4-17  certificate [4, 2, 3, 0, 17, 18, 19, 16]
    add 4-18  certificate [4, 0, 1, 3, 18, 16, 17, 19]
    add 4-19  certificate [4, 0, 1, 2, 19, 16, 17, 18]
    add 5-12  certificate [5, 0, 2, 1, 12, 4, 14, 13]
    add 5-13  certificate [5, 0, 2, 3, 13, 1, 4, 6]
    add 5-14  certificate [5, 0, 1, 2, 14, 12, 13, 4]
    add 5-15  certificate [5, 0, 1, 2, 15, 3, 4, 6]
    add 5-16  certificate [5, 0, 2, 1, 16, 4, 18, 17]
    add 5-17  certificate [5, 0, 2, 3, 17, 1, 4, 6]
    add 5-18  certificate [5, 0, 1, 2, 18, 16, 17, 4]
    add 5-19  certificate [5, 0, 1, 2, 19, 3, 4, 6]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 3, 4, 5]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 4, 5, 3]
    add 6-18  certificate [6, 0, 1, 2, 18, 4, 5, 3]
    add 6-19  certificate [6, 0, 1, 2, 19, 3, 4, 5]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 4, 5, 3]
    add 7-15  certificate [7, 0, 1, 2, 15, 3, 4, 5]
    add 7-16  certificate [7, 0, 1, 2, 16, 4, 5, 3]
    add 7-17  certificate [7, 0, 1, 2, 17, 4, 5, 3]
    add 7-18  certificate [7, 0, 1, 2, 18, 4, 5, 3]
    add 7-19  certificate [7, 0, 1, 2, 19, 3, 4, 5]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 3, 4, 5]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 4, 5, 3]
    add 8-18  certificate [8, 0, 1, 2, 18, 4, 5, 3]
    add 8-19  certificate [8, 0, 1, 2, 19, 3, 4, 5]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 4, 5, 3]
    add 9-15  certificate [9, 0, 1, 2, 15, 3, 4, 5]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 4, 5, 3]
    add 9-18  certificate [9, 0, 1, 2, 18, 4, 5, 3]
    add 9-19  certificate [9, 0, 1, 2, 19, 3, 4, 5]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 4, 5, 3]
    add 10-15  certificate [10, 0, 1, 2, 15, 3, 4, 5]
    add 10-16  certificate [10, 0, 1, 2, 16, 4, 5, 3]
    add 10-17  certificate [10, 0, 1, 2, 17, 4, 5, 3]
    add 10-18  certificate [10, 0, 1, 2, 18, 4, 5, 3]
    add 10-19  certificate [10, 0, 1, 2, 19, 3, 4, 5]
    add 11-12  certificate [11, 0, 1, 2, 12, 4, 5, 3]
    add 11-13  certificate [11, 0, 1, 2, 13, 4, 5, 3]
    add 11-14  certificate [11, 0, 1, 2, 14, 4, 5, 3]
    add 11-15  certificate [11, 0, 1, 2, 15, 3, 4, 5]
    add 11-16  certificate [11, 0, 1, 2, 16, 4, 5, 3]
    add 11-17  certificate [11, 0, 1, 2, 17, 4, 5, 3]
    add 11-18  certificate [11, 0, 1, 2, 18, 4, 5, 3]
    add 11-19  certificate [11, 0, 1, 2, 19, 3, 4, 5]
    add 12-13  certificate [12, 0, 4, 1, 13, 5, 6, 2]
    add 12-16  certificate [12, 0, 4, 1, 16, 5, 6, 2]
    add 12-17  certificate [12, 0, 4, 1, 17, 5, 6, 2]
    add 12-18  certificate [12, 0, 4, 1, 18, 2, 5, 3]
    add 12-19  certificate [12, 0, 4, 1, 19, 3, 5, 2]
    add 13-16  certificate [13, 1, 4, 0, 16, 5, 6, 2]
    add 13-17  certificate [13, 1, 4, 0, 17, 5, 6, 2]
    add 13-18  certificate [13, 1, 4, 0, 18, 2, 5, 3]
    add 13-19  certificate [13, 1, 4, 0, 19, 3, 5, 2]
    add 14-15  certificate [14, 2, 4, 0, 15, 3, 5, 1]
    add 14-16  certificate [14, 2, 4, 0, 16, 5, 6, 1]
    add 14-17  certificate [14, 2, 4, 0, 17, 1, 5, 3]
    add 14-18  certificate [14, 2, 4, 0, 18, 5, 6, 1]
    add 14-19  certificate [14, 2, 4, 0, 19, 3, 5, 1]
    add 15-16  certificate [15, 3, 4, 0, 16, 5, 6, 1]
    add 15-17  certificate [15, 3, 4, 0, 17, 1, 5, 2]
    add 15-18  certificate [15, 3, 4, 0, 18, 2, 5, 1]
    add 15-19  certificate [15, 3, 4, 0, 19, 5, 6, 1]
    add 16-17  certificate [16, 0, 4, 1, 17, 5, 6, 2]
    add 18-19  certificate [18, 2, 4, 0, 19, 3, 5, 1]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 0-18  certificate [0, 1, 2, 3, 18, 4, 5, 6]
    add 0-19  certificate [0, 1, 2, 3, 19, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 1-18  certificate [1, 0, 2, 3, 18, 4, 5, 6]
    add 1-19  certificate [1, 0, 2, 3, 19, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 2-17  certificate [2, 0, 1, 3, 17, 4, 5, 6]
    add 2-19  certificate [2, 0, 1, 3, 19, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
    add 3-17  certificate [3, 0, 1, 2, 17, 4, 5, 6]
    add 3-18  certificate [3, 0, 1, 2, 18, 4, 5, 6]
composite n=21: S_9 + 3 gadget(s) at 0,1,2,3; 37 edges; 173 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 0, 4, 5]
    add 7-8  certificate [7, 3, 5, 0, 8, 2, 4, 1]
    add 9-12  certificate [9, 0, 11, 2, 12, 3, 10, 1]
    add 13-16  certificate [13, 0, 15, 2, 16, 3, 14, 1]
    add 17-20  certificate [17, 0, 19, 2, 20, 3, 18, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 8]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 8, 4]
    add 1-8  certificate [1, 0, 3, 2, 8, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 8, 4]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-9  certificate [4, 2, 3, 1, 9, 11, 12, 10]
    add 4-10  certificate [4, 2, 3, 0, 10, 11, 12, 9]
    add 4-11  certificate [4, 0, 1, 3, 11, 9, 10, 12]
    add 4-12  certificate [4, 0, 1, 2, 12, 9, 10, 11]
    add 4-13  certificate [4, 2, 3, 1, 13, 15, 16, 14]
    add 4-14  certificate [4, 2, 3, 0, 14, 15, 16, 13]
    add 4-15  certificate [4, 0, 1, 3, 15, 13, 14, 16]
    add 4-16  certificate [4, 0, 1, 2, 16, 13, 14, 15]
    add 4-17  certificate [4, 2, 3, 1, 17, 19, 20, 18]
    add 4-18  certificate [4, 2, 3, 0, 18, 19, 20, 17]
    add 4-19  certificate [4, 0, 1, 3, 19, 17, 18, 20]
    add 4-20  certificate [4, 0, 1, 2, 20, 17, 18, 19]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 2, 1, 9, 4, 11, 10]
    add 5-10  certificate [5, 0, 2, 3, 10, 1, 4, 6]
    add 5-11  certificate [5, 0, 1, 2, 11, 9, 10, 4]
    add 5-12  certificate [5, 0, 1, 2, 12, 3, 4, 6]
    add 5-13  certificate [5, 0, 2, 1, 13, 4, 15, 14]
    add 5-14  certificate [5, 0, 2, 3, 14, 1, 4, 6]
    add 5-15  certificate [5, 0, 1, 2, 15, 13, 14, 4]
    add 5-16  certificate [5, 0, 1, 2, 16, 3, 4, 6]
    add 5-17  certificate [5, 0, 2, 1, 17, 4, 19, 18]
    add 5-18  certificate [5, 0, 2, 3, 18, 1, 4, 6]
    add 5-19  certificate [5, 0, 1, 2, 19, 17, 18, 4]
    add 5-20  certificate [5, 0, 1, 2, 20, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 4, 5, 3]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 3, 4, 5]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 3, 4, 5]
    add 6-17  certificate [6, 0, 1, 2, 17, 4, 5, 3]
    add 6-18  certificate [6, 0, 1, 2, 18, 4, 5, 3]
    add 6-19  certificate [6, 0, 1, 2, 19, 4, 5, 3]
    add 6-20  certificate [6, 0, 1, 2, 20, 3, 4, 5]
    add 7-9  certificate [7, 1, 2, 0, 9, 4, 5, 3]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 3, 4, 5]
    add 7-13  certificate [7, 1, 2, 0, 13, 4, 5, 3]
    add 7-14  certificate [7, 1, 2, 0, 14, 4, 5, 3]
    add 7-15  certificate [7, 1, 2, 0, 15, 4, 5, 3]
    add 7-16  certificate [7, 1, 2, 0, 16, 3, 4, 5]
    add 7-17  certificate [7, 1, 2, 0, 17, 4, 5, 3]
    add 7-18  certificate [7, 1, 2, 0, 18, 4, 5, 3]
    add 7-19  certificate [7, 1, 2, 0, 19, 4, 5, 3]
    add 7-20  certificate [7, 1, 2, 0, 20, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 4, 5, 3]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 3, 4, 5]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 3, 4, 5]
    add 8-17  certificate [8, 0, 1, 2, 17, 4, 5, 3]
    add 8-18  certificate [8, 0, 1, 2, 18, 4, 5, 3]
    add 8-19  certificate [8, 0, 1, 2, 19, 4, 5, 3]
    add 8-20  certificate [8, 0, 1, 2, 20, 3, 4, 5]
    add 9-10  certificate [9, 0, 4, 1, 10, 5, 6, 2]
    add 9-13  certificate [9, 0, 4, 1, 13, 5, 6, 2]
    add 9-14  certificate [9, 0, 4, 1, 14, 5, 6, 2]
    add 9-15  certificate [9, 0, 4, 1, 15, 2, 5, 3]
    add 9-16  certificate [9, 0, 4, 1, 16, 3, 5, 2]
    add 9-17  certificate [9, 0, 4, 1, 17, 5, 6, 2]
    add 9-18  certificate [9, 0, 4, 1, 18, 5, 6, 2]
    add 9-19  certificate [9, 0, 4, 1, 19, 2, 5, 3]
    add 9-20  certificate [9, 0, 4, 1, 20, 3, 5, 2]
    add 10-13  certificate [10, 1, 4, 0, 13, 5, 6, 2]
    add 10-14  certificate [10, 1, 4, 0, 14, 5, 6, 2]
    add 10-15  certificate [10, 1, 4, 0, 15, 2, 5, 3]
    add 10-16  certificate [10, 1, 4, 0, 16, 3, 5, 2]
    add 10-17  certificate [10, 1, 4, 0, 17, 5, 6, 2]
    add 10-18  certificate [10, 1, 4, 0, 18, 5, 6, 2]
    add 10-19  certificate [10, 1, 4, 0, 19, 2, 5, 3]
    add 10-20  certificate [10, 1, 4, 0, 20, 3, 5, 2]
    add 11-12  certificate [11, 2, 4, 0, 12, 3, 5, 1]
    add 11-13  certificate [11, 2, 4, 0, 13, 5, 6, 1]
    add 11-14  certificate [11, 2, 4, 0, 14, 1, 5, 3]
    add 11-15  certificate [11, 2, 4, 0, 15, 5, 6, 1]
    add 11-16  certificate [11, 2, 4, 0, 16, 3, 5, 1]
    add 11-17  certificate [11, 2, 4, 0, 17, 5, 6, 1]
    add 11-18  certificate [11, 2, 4, 0, 18, 1, 5, 3]
    add 11-19  certificate [11, 2, 4, 0, 19, 5, 6, 1]
    add 11-20  certificate [11, 2, 4, 0, 20, 3, 5, 1]
    add 12-13  certificate [12, 3, 4, 0, 13, 5, 6, 1]
    add 12-14  certificate [12, 3, 4, 0, 14, 1, 5, 2]
    add 12-15  certificate [12, 3, 4, 0, 15, 2, 5, 1]
    add 12-16  certificate [12, 3, 4, 0, 16, 5, 6, 1]
    add 12-17  certificate [12, 3, 4, 0, 17, 5, 6, 1]
    add 12-18  certificate [12, 3, 4, 0, 18, 1, 5, 2]
    add 12-19  certificate [12, 3, 4, 0, 19, 2, 5, 1]
    add 12-20  certificate [12, 3, 4, 0, 20, 5, 6, 1]
    add 13-14  certificate [13, 0, 4, 1, 14, 5, 6, 2]
    add 13-17  certificate [13, 0, 4, 1, 17, 5, 6, 2]
    add 13-18  certificate [13, 0, 4, 1, 18, 5, 6, 2]
    add 13-19  certificate [13, 0, 4, 1, 19, 2, 5, 3]
    add 13-20  certificate [13, 0, 4, 1, 20, 3, 5, 2]
    add 14-17  certificate [14, 1, 4, 0, 17, 5, 6, 2]
    add 14-18  certificate [14, 1, 4, 0, 18, 5, 6, 2]
    add 14-19  certificate [14, 1, 4, 0, 19, 2, 5, 3]
    add 14-20  certificate [14, 1, 4, 0, 20, 3, 5, 2]
    add 15-16  certificate [15, 2, 4, 0, 16, 3, 5, 1]
    add 15-17  certificate [15, 2, 4, 0, 17, 5, 6, 1]
    add 15-18  certificate [15, 2, 4, 0, 18, 1, 5, 3]
    add 15-19  certificate [15, 2, 4, 0, 19, 5, 6, 1]
    add 15-20  certificate [15, 2, 4, 0, 20, 3, 5, 1]
    add 16-17  certificate [16, 3, 4, 0, 17, 5, 6, 1]
    add 16-18  certificate [16, 3, 4, 0, 18, 1, 5, 2]
    add 16-19  certificate [16, 3, 4, 0, 19, 2, 5, 1]
    add 16-20  certificate [16, 3, 4, 0, 20, 5, 6, 1]
    add 17-18  certificate [17, 0, 4, 1, 18, 5, 6, 2]
    add 19-20  certificate [19, 2, 4, 0, 20, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 0-18  certificate [0, 1, 2, 3, 18, 4, 5, 6]
    add 0-19  certificate [0, 1, 2, 3, 19, 4, 5, 6]
    add 0-20  certificate [0, 1, 2, 3, 20, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 1-17  certificate [1, 0, 2, 3, 17, 4, 5, 6]
    add 1-19  certificate [1, 0, 2, 3, 19, 4, 5, 6]
    add 1-20  certificate [1, 0, 2, 3, 20, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 2-17  certificate [2, 0, 1, 3, 17, 4, 5, 6]
    add 2-18  certificate [2, 0, 1, 3, 18, 4, 5, 6]
    add 2-20  certificate [2, 0, 1, 3, 20, 4, 5, 6]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
    add 3-17  certificate [3, 0, 1, 2, 17, 4, 5, 6]
    add 3-18  certificate [3, 0, 1, 2, 18, 4, 5, 6]
    add 3-19  certificate [3, 0, 1, 2, 19, 4, 5, 6]
composite n=22: S_10 + 3 gadget(s) at 0,1,2,3; 39 edges; 192 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 4-9  certificate [4, 5, 6, 7, 9, 0, 2, 3]
    add 7-9  certificate [7, 3, 5, 0, 9, 2, 4, 1]
    add 10-13  certificate [10, 0, 12, 2, 13, 3, 11, 1]
    add 14-17  certificate [14, 0, 16, 2, 17, 3, 15, 1]
    add 18-21  certificate [18, 0, 20, 2, 21, 3, 19, 1]
    add 0-6  certificate [0, 1, 3, 2, 6, 4, 7, 9]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 9]
    add 1-7  certificate [1, 0, 2, 6, 7, 5, 9, 4]
    add 1-9  certificate [1, 0, 3, 2, 9, 4, 7, 6]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 2-7  certificate [2, 0, 1, 5, 7, 6, 9, 4]
    add 2-8  certificate [2, 3, 5, 7, 8, 0, 1, 6]
    add 3-4  certificate [3, 0, 1, 2, 4, 5, 6, 7]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 7, 6]
    add 3-6  certificate [3, 0, 1, 2, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 4, 5, 8, 1, 2, 7]
    add 3-9  certificate [3, 0, 1, 2, 9, 4, 7, 5]
    add 4-7  certificate [4, 0, 1, 2, 7, 5, 6, 3]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-10  certificate [4, 2, 3, 1, 10, 12, 13, 11]
    add 4-11  certificate [4, 2, 3, 0, 11, 12, 13, 10]
    add 4-12  certificate [4, 0, 1, 3, 12, 10, 11, 13]
    add 4-13  certificate [4, 0, 1, 2, 13, 10, 11, 12]
    add 4-14  certificate [4, 2, 3, 1, 14, 16, 17, 15]
    add 4-15  certificate [4, 2, 3, 0, 15, 16, 17, 14]
    add 4-16  certificate [4, 0, 1, 3, 16, 14, 15, 17]
    add 4-17  certificate [4, 0, 1, 2, 17, 14, 15, 16]
    add 4-18  certificate [4, 2, 3, 1, 18, 20, 21, 19]
    add 4-19  certificate [4, 2, 3, 0, 19, 20, 21, 18]
    add 4-20  certificate [4, 0, 1, 3, 20, 18, 19, 21]
    add 4-21  certificate [4, 0, 1, 2, 21, 18, 19, 20]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 5-10  certificate [5, 0, 2, 1, 10, 4, 12, 11]
    add 5-11  certificate [5, 0, 2, 3, 11, 1, 4, 6]
    add 5-12  certificate [5, 0, 1, 2, 12, 10, 11, 4]
    add 5-13  certificate [5, 0, 1, 2, 13, 3, 4, 6]
    add 5-14  certificate [5, 0, 2, 1, 14, 4, 16, 15]
    add 5-15  certificate [5, 0, 2, 3, 15, 1, 4, 6]
    add 5-16  certificate [5, 0, 1, 2, 16, 14, 15, 4]
    add 5-17  certificate [5, 0, 1, 2, 17, 3, 4, 6]
    add 5-18  certificate [5, 0, 2, 1, 18, 4, 20, 19]
    add 5-19  certificate [5, 0, 2, 3, 19, 1, 4, 6]
    add 5-20  certificate [5, 0, 1, 2, 20, 18, 19, 4]
    add 5-21  certificate [5, 0, 1, 2, 21, 3, 4, 6]
    add 6-8  certificate [6, 0, 1, 2, 8, 3, 4, 5]
    add 6-9  certificate [6, 0, 1, 2, 9, 3, 4, 5]
    add 6-10  certificate [6, 0, 1, 2, 10, 4, 5, 3]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 3, 4, 5]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 3, 4, 5]
    add 6-18  certificate [6, 0, 1, 2, 18, 4, 5, 3]
    add 6-19  certificate [6, 0, 1, 2, 19, 4, 5, 3]
    add 6-20  certificate [6, 0, 1, 2, 20, 4, 5, 3]
    add 6-21  certificate [6, 0, 1, 2, 21, 3, 4, 5]
    add 7-8  certificate [7, 1, 2, 0, 8, 3, 4, 5]
    add 7-10  certificate [7, 1, 2, 0, 10, 4, 5, 3]
    add 7-11  certificate [7, 1, 2, 0, 11, 4, 5, 3]
    add 7-12  certificate [7, 1, 2, 0, 12, 4, 5, 3]
    add 7-13  certificate [7, 1, 2, 0, 13, 3, 4, 5]
    add 7-14  certificate [7, 1, 2, 0, 14, 4, 5, 3]
    add 7-15  certificate [7, 1, 2, 0, 15, 4, 5, 3]
    add 7-16  certificate [7, 1, 2, 0, 16, 4, 5, 3]
    add 7-17  certificate [7, 1, 2, 0, 17, 3, 4, 5]
    add 7-18  certificate [7, 1, 2, 0, 18, 4, 5, 3]
    add 7-19  certificate [7, 1, 2, 0, 19, 4, 5, 3]
    add 7-20  certificate [7, 1, 2, 0, 20, 4, 5, 3]
    add 7-21  certificate [7, 1, 2, 0, 21, 3, 4, 5]
    add 8-9  certificate [8, 0, 1, 2, 9, 3, 4, 5]
    add 8-10  certificate [8, 0, 1, 2, 10, 4, 5, 3]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 3, 4, 5]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 3, 4, 5]
    add 8-18  certificate [8, 0, 1, 2, 18, 4, 5, 3]
    add 8-19  certificate [8, 0, 1, 2, 19, 4, 5, 3]
    add 8-20  certificate [8, 0, 1, 2, 20, 4, 5, 3]
    add 8-21  certificate [8, 0, 1, 2, 21, 3, 4, 5]
    add 9-10  certificate [9, 0, 1, 2, 10, 4, 5, 3]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 3, 4, 5]
    add 9-14  certificate [9, 0, 1, 2, 14, 4, 5, 3]
    add 9-15  certificate [9, 0, 1, 2, 15, 4, 5, 3]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 3, 4, 5]
    add 9-18  certificate [9, 0, 1, 2, 18, 4, 5, 3]
    add 9-19  certificate [9, 0, 1, 2, 19, 4, 5, 3]
    add 9-20  certificate [9, 0, 1, 2, 20, 4, 5, 3]
    add 9-21  certificate [9, 0, 1, 2, 21, 3, 4, 5]
    add 10-11  certificate [10, 0, 4, 1, 11, 5, 6, 2]
    add 10-14  certificate [10, 0, 4, 1, 14, 5, 6, 2]
    add 10-15  certificate [10, 0, 4, 1, 15, 5, 6, 2]
    add 10-16  certificate [10, 0, 4, 1, 16, 2, 5, 3]
    add 10-17  certificate [10, 0, 4, 1, 17, 3, 5, 2]
    add 10-18  certificate [10, 0, 4, 1, 18, 5, 6, 2]
    add 10-19  certificate [10, 0, 4, 1, 19, 5, 6, 2]
    add 10-20  certificate [10, 0, 4, 1, 20, 2, 5, 3]
    add 10-21  certificate [10, 0, 4, 1, 21, 3, 5, 2]
    add 11-14  certificate [11, 1, 4, 0, 14, 5, 6, 2]
    add 11-15  certificate [11, 1, 4, 0, 15, 5, 6, 2]
    add 11-16  certificate [11, 1, 4, 0, 16, 2, 5, 3]
    add 11-17  certificate [11, 1, 4, 0, 17, 3, 5, 2]
    add 11-18  certificate [11, 1, 4, 0, 18, 5, 6, 2]
    add 11-19  certificate [11, 1, 4, 0, 19, 5, 6, 2]
    add 11-20  certificate [11, 1, 4, 0, 20, 2, 5, 3]
    add 11-21  certificate [11, 1, 4, 0, 21, 3, 5, 2]
    add 12-13  certificate [12, 2, 4, 0, 13, 3, 5, 1]
    add 12-14  certificate [12, 2, 4, 0, 14, 5, 6, 1]
    add 12-15  certificate [12, 2, 4, 0, 15, 1, 5, 3]
    add 12-16  certificate [12, 2, 4, 0, 16, 5, 6, 1]
    add 12-17  certificate [12, 2, 4, 0, 17, 3, 5, 1]
    add 12-18  certificate [12, 2, 4, 0, 18, 5, 6, 1]
    add 12-19  certificate [12, 2, 4, 0, 19, 1, 5, 3]
    add 12-20  certificate [12, 2, 4, 0, 20, 5, 6, 1]
    add 12-21  certificate [12, 2, 4, 0, 21, 3, 5, 1]
    add 13-14  certificate [13, 3, 4, 0, 14, 5, 6, 1]
    add 13-15  certificate [13, 3, 4, 0, 15, 1, 5, 2]
    add 13-16  certificate [13, 3, 4, 0, 16, 2, 5, 1]
    add 13-17  certificate [13, 3, 4, 0, 17, 5, 6, 1]
    add 13-18  certificate [13, 3, 4, 0, 18, 5, 6, 1]
    add 13-19  certificate [13, 3, 4, 0, 19, 1, 5, 2]
    add 13-20  certificate [13, 3, 4, 0, 20, 2, 5, 1]
    add 13-21  certificate [13, 3, 4, 0, 21, 5, 6, 1]
    add 14-15  certificate [14, 0, 4, 1, 15, 5, 6, 2]
    add 14-18  certificate [14, 0, 4, 1, 18, 5, 6, 2]
    add 14-19  certificate [14, 0, 4, 1, 19, 5, 6, 2]
    add 14-20  certificate [14, 0, 4, 1, 20, 2, 5, 3]
    add 14-21  certificate [14, 0, 4, 1, 21, 3, 5, 2]
    add 15-18  certificate [15, 1, 4, 0, 18, 5, 6, 2]
    add 15-19  certificate [15, 1, 4, 0, 19, 5, 6, 2]
    add 15-20  certificate [15, 1, 4, 0, 20, 2, 5, 3]
    add 15-21  certificate [15, 1, 4, 0, 21, 3, 5, 2]
    add 16-17  certificate [16, 2, 4, 0, 17, 3, 5, 1]
    add 16-18  certificate [16, 2, 4, 0, 18, 5, 6, 1]
    add 16-19  certificate [16, 2, 4, 0, 19, 1, 5, 3]
    add 16-20  certificate [16, 2, 4, 0, 20, 5, 6, 1]
    add 16-21  certificate [16, 2, 4, 0, 21, 3, 5, 1]
    add 17-18  certificate [17, 3, 4, 0, 18, 5, 6, 1]
    add 17-19  certificate [17, 3, 4, 0, 19, 1, 5, 2]
    add 17-20  certificate [17, 3, 4, 0, 20, 2, 5, 1]
    add 17-21  certificate [17, 3, 4, 0, 21, 5, 6, 1]
    add 18-19  certificate [18, 0, 4, 1, 19, 5, 6, 2]
    add 20-21  certificate [20, 2, 4, 0, 21, 3, 5, 1]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 5, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 4, 5, 6]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 0-19  certificate [0, 1, 2, 3, 19, 4, 5, 6]
    add 0-20  certificate [0, 1, 2, 3, 20, 4, 5, 6]
    add 0-21  certificate [0, 1, 2, 3, 21, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 1-17  certificate [1, 0, 2, 3, 17, 4, 5, 6]
    add 1-18  certificate [1, 0, 2, 3, 18, 4, 5, 6]
    add 1-20  certificate [1, 0, 2, 3, 20, 4, 5, 6]
    add 1-21  certificate [1, 0, 2, 3, 21, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-17  certificate [2, 0, 1, 3, 17, 4, 5, 6]
    add 2-18  certificate [2, 0, 1, 3, 18, 4, 5, 6]
    add 2-19  certificate [2, 0, 1, 3, 19, 4, 5, 6]
    add 2-21  certificate [2, 0, 1, 3, 21, 4, 5, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
    add 3-18  certificate [3, 0, 1, 2, 18, 4, 5, 6]
    add 3-19  certificate [3, 0, 1, 2, 19, 4, 5, 6]
    add 3-20  certificate [3, 0, 1, 2, 20, 4, 5, 6]
composite n=23: S_11 + 3 gadget(s) at 0,1,2,3; 40 edges; 213 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 8-10  certificate [8, 1, 9, 3, 10, 5, 2, 0]
    add 2-7  certificate [2, 9, 10, 8, 7, 3, 5, 1]
    add 7-8  certificate [7, 2, 3, 0, 8, 10, 1, 5]
    add 0-8  certificate [0, 2, 3, 7, 8, 10, 1, 5]
    add 1-2  certificate [1, 3, 5, 0, 2, 7, 10, 8]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 2-8  certificate [2, 0, 6, 4, 8, 1, 7, 5]
    add 3-4  certificate [3, 0, 2, 8, 4, 5, 6, 7]
    add 3-5  certificate [3, 2, 4, 0, 5, 7, 1, 8]
    add 3-6  certificate [3, 0, 2, 1, 6, 4, 7, 5]
    add 3-8  certificate [3, 0, 5, 4, 8, 2, 7, 6]
    add 3-10  certificate [3, 0, 1, 2, 10, 5, 8, 7]
    add 4-7  certificate [4, 0, 1, 2, 7, 3, 5, 10]
    add 4-8  certificate [4, 0, 1, 5, 8, 2, 3, 7]
    add 4-9  certificate [4, 0, 1, 2, 9, 3, 8, 7]
    add 4-10  certificate [4, 0, 1, 2, 10, 3, 5, 7]
    add 5-6  certificate [5, 0, 1, 2, 6, 3, 4, 7]
    add 5-8  certificate [5, 0, 1, 2, 8, 3, 4, 6]
    add 5-9  certificate [5, 0, 1, 2, 9, 3, 4, 6]
    add 6-8  certificate [6, 2, 3, 0, 8, 1, 4, 5]
    add 6-9  certificate [6, 2, 3, 0, 9, 8, 4, 1]
    add 6-10  certificate [6, 2, 3, 0, 10, 8, 4, 1]
    add 7-9  certificate [7, 2, 3, 0, 9, 6, 4, 5]
    add 7-10  certificate [7, 2, 3, 0, 10, 6, 4, 5]
    add 9-10  certificate [9, 2, 3, 0, 10, 6, 4, 5]
    add 11-14  certificate [11, 0, 13, 2, 14, 3, 12, 1]
    add 15-18  certificate [15, 0, 17, 2, 18, 3, 16, 1]
    add 19-22  certificate [19, 0, 21, 2, 22, 3, 20, 1]
    add 0-6  certificate [0, 1, 2, 3, 6, 4, 7, 5]
    add 0-7  certificate [0, 1, 2, 3, 7, 4, 6, 5]
    add 0-9  certificate [0, 1, 2, 3, 9, 4, 6, 5]
    add 0-10  certificate [0, 1, 2, 3, 10, 4, 6, 5]
    add 1-6  certificate [1, 0, 2, 3, 6, 4, 7, 5]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 6, 5]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 6, 5]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 6, 5]
    add 2-4  certificate [2, 0, 1, 3, 4, 5, 6, 7]
    add 2-5  certificate [2, 0, 1, 3, 5, 4, 6, 7]
    add 4-11  certificate [4, 2, 3, 1, 11, 13, 14, 12]
    add 4-12  certificate [4, 2, 3, 0, 12, 13, 14, 11]
    add 4-13  certificate [4, 0, 1, 3, 13, 11, 12, 14]
    add 4-14  certificate [4, 0, 1, 2, 14, 11, 12, 13]
    add 4-15  certificate [4, 2, 3, 1, 15, 17, 18, 16]
    add 4-16  certificate [4, 2, 3, 0, 16, 17, 18, 15]
    add 4-17  certificate [4, 0, 1, 3, 17, 15, 16, 18]
    add 4-18  certificate [4, 0, 1, 2, 18, 15, 16, 17]
    add 4-19  certificate [4, 2, 3, 1, 19, 21, 22, 20]
    add 4-20  certificate [4, 2, 3, 0, 20, 21, 22, 19]
    add 4-21  certificate [4, 0, 1, 3, 21, 19, 20, 22]
    add 4-22  certificate [4, 0, 1, 2, 22, 19, 20, 21]
    add 5-11  certificate [5, 0, 2, 1, 11, 4, 13, 12]
    add 5-12  certificate [5, 0, 2, 3, 12, 1, 4, 6]
    add 5-13  certificate [5, 0, 1, 2, 13, 11, 12, 4]
    add 5-14  certificate [5, 0, 1, 2, 14, 3, 4, 6]
    add 5-15  certificate [5, 0, 2, 1, 15, 4, 17, 16]
    add 5-16  certificate [5, 0, 2, 3, 16, 1, 4, 6]
    add 5-17  certificate [5, 0, 1, 2, 17, 15, 16, 4]
    add 5-18  certificate [5, 0, 1, 2, 18, 3, 4, 6]
    add 5-19  certificate [5, 0, 2, 1, 19, 4, 21, 20]
    add 5-20  certificate [5, 0, 2, 3, 20, 1, 4, 6]
    add 5-21  certificate [5, 0, 1, 2, 21, 19, 20, 4]
    add 5-22  certificate [5, 0, 1, 2, 22, 3, 4, 6]
    add 6-11  certificate [6, 0, 1, 2, 11, 4, 5, 3]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 3, 4, 5]
    add 6-15  certificate [6, 0, 1, 2, 15, 4, 5, 3]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 4, 5, 3]
    add 6-18  certificate [6, 0, 1, 2, 18, 3, 4, 5]
    add 6-19  certificate [6, 0, 1, 2, 19, 4, 5, 3]
    add 6-20  certificate [6, 0, 1, 2, 20, 4, 5, 3]
    add 6-21  certificate [6, 0, 1, 2, 21, 4, 5, 3]
    add 6-22  certificate [6, 0, 1, 2, 22, 3, 4, 5]
    add 7-11  certificate [7, 0, 1, 2, 11, 4, 5, 3]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 3, 4, 5]
    add 7-15  certificate [7, 0, 1, 2, 15, 4, 5, 3]
    add 7-16  certificate [7, 0, 1, 2, 16, 4, 5, 3]
    add 7-17  certificate [7, 0, 1, 2, 17, 4, 5, 3]
    add 7-18  certificate [7, 0, 1, 2, 18, 3, 4, 5]
    add 7-19  certificate [7, 0, 1, 2, 19, 4, 5, 3]
    add 7-20  certificate [7, 0, 1, 2, 20, 4, 5, 3]
    add 7-21  certificate [7, 0, 1, 2, 21, 4, 5, 3]
    add 7-22  certificate [7, 0, 1, 2, 22, 3, 4, 5]
    add 8-11  certificate [8, 0, 1, 2, 11, 4, 5, 3]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 3, 4, 5]
    add 8-15  certificate [8, 0, 1, 2, 15, 4, 5, 3]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 4, 5, 3]
    add 8-18  certificate [8, 0, 1, 2, 18, 3, 4, 5]
    add 8-19  certificate [8, 0, 1, 2, 19, 4, 5, 3]
    add 8-20  certificate [8, 0, 1, 2, 20, 4, 5, 3]
    add 8-21  certificate [8, 0, 1, 2, 21, 4, 5, 3]
    add 8-22  certificate [8, 0, 1, 2, 22, 3, 4, 5]
    add 9-11  certificate [9, 0, 1, 2, 11, 4, 5, 3]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 3, 4, 5]
    add 9-15  certificate [9, 0, 1, 2, 15, 4, 5, 3]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 4, 5, 3]
    add 9-18  certificate [9, 0, 1, 2, 18, 3, 4, 5]
    add 9-19  certificate [9, 0, 1, 2, 19, 4, 5, 3]
    add 9-20  certificate [9, 0, 1, 2, 20, 4, 5, 3]
    add 9-21  certificate [9, 0, 1, 2, 21, 4, 5, 3]
    add 9-22  certificate [9, 0, 1, 2, 22, 3, 4, 5]
    add 10-11  certificate [10, 0, 1, 2, 11, 4, 5, 3]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 3, 4, 5]
    add 10-15  certificate [10, 0, 1, 2, 15, 4, 5, 3]
    add 10-16  certificate [10, 0, 1, 2, 16, 4, 5, 3]
    add 10-17  certificate [10, 0, 1, 2, 17, 4, 5, 3]
    add 10-18  certificate [10, 0, 1, 2, 18, 3, 4, 5]
    add 10-19  certificate [10, 0, 1, 2, 19, 4, 5, 3]
    add 10-20  certificate [10, 0, 1, 2, 20, 4, 5, 3]
    add 10-21  certificate [10, 0, 1, 2, 21, 4, 5, 3]
    add 10-22  certificate [10, 0, 1, 2, 22, 3, 4, 5]
    add 11-12  certificate [11, 0, 4, 1, 12, 5, 6, 2]
    add 11-15  certificate [11, 0, 4, 1, 15, 5, 6, 2]
    add 11-16  certificate [11, 0, 4, 1, 16, 5, 6, 2]
    add 11-17  certificate [11, 0, 4, 1, 17, 2, 5, 3]
    add 11-18  certificate [11, 0, 4, 1, 18, 3, 5, 2]
    add 11-19  certificate [11, 0, 4, 1, 19, 5, 6, 2]
    add 11-20  certificate [11, 0, 4, 1, 20, 5, 6, 2]
    add 11-21  certificate [11, 0, 4, 1, 21, 2, 5, 3]
    add 11-22  certificate [11, 0, 4, 1, 22, 3, 5, 2]
    add 12-15  certificate [12, 1, 4, 0, 15, 5, 6, 2]
    add 12-16  certificate [12, 1, 4, 0, 16, 5, 6, 2]
    add 12-17  certificate [12, 1, 4, 0, 17, 2, 5, 3]
    add 12-18  certificate [12, 1, 4, 0, 18, 3, 5, 2]
    add 12-19  certificate [12, 1, 4, 0, 19, 5, 6, 2]
    add 12-20  certificate [12, 1, 4, 0, 20, 5, 6, 2]
    add 12-21  certificate [12, 1, 4, 0, 21, 2, 5, 3]
    add 12-22  certificate [12, 1, 4, 0, 22, 3, 5, 2]
    add 13-14  certificate [13, 2, 4, 0, 14, 3, 5, 1]
    add 13-15  certificate [13, 2, 4, 0, 15, 5, 6, 1]
    add 13-16  certificate [13, 2, 4, 0, 16, 1, 5, 3]
    add 13-17  certificate [13, 2, 4, 0, 17, 5, 6, 1]
    add 13-18  certificate [13, 2, 4, 0, 18, 3, 5, 1]
    add 13-19  certificate [13, 2, 4, 0, 19, 5, 6, 1]
    add 13-20  certificate [13, 2, 4, 0, 20, 1, 5, 3]
    add 13-21  certificate [13, 2, 4, 0, 21, 5, 6, 1]
    add 13-22  certificate [13, 2, 4, 0, 22, 3, 5, 1]
    add 14-15  certificate [14, 3, 4, 0, 15, 5, 6, 1]
    add 14-16  certificate [14, 3, 4, 0, 16, 1, 5, 2]
    add 14-17  certificate [14, 3, 4, 0, 17, 2, 5, 1]
    add 14-18  certificate [14, 3, 4, 0, 18, 5, 6, 1]
    add 14-19  certificate [14, 3, 4, 0, 19, 5, 6, 1]
    add 14-20  certificate [14, 3, 4, 0, 20, 1, 5, 2]
    add 14-21  certificate [14, 3, 4, 0, 21, 2, 5, 1]
    add 14-22  certificate [14, 3, 4, 0, 22, 5, 6, 1]
    add 15-16  certificate [15, 0, 4, 1, 16, 5, 6, 2]
    add 15-19  certificate [15, 0, 4, 1, 19, 5, 6, 2]
    add 15-20  certificate [15, 0, 4, 1, 20, 5, 6, 2]
    add 15-21  certificate [15, 0, 4, 1, 21, 2, 5, 3]
    add 15-22  certificate [15, 0, 4, 1, 22, 3, 5, 2]
    add 16-19  certificate [16, 1, 4, 0, 19, 5, 6, 2]
    add 16-20  certificate [16, 1, 4, 0, 20, 5, 6, 2]
    add 16-21  certificate [16, 1, 4, 0, 21, 2, 5, 3]
    add 16-22  certificate [16, 1, 4, 0, 22, 3, 5, 2]
    add 17-18  certificate [17, 2, 4, 0, 18, 3, 5, 1]
    add 17-19  certificate [17, 2, 4, 0, 19, 5, 6, 1]
    add 17-20  certificate [17, 2, 4, 0, 20, 1, 5, 3]
    add 17-21  certificate [17, 2, 4, 0, 21, 5, 6, 1]
    add 17-22  certificate [17, 2, 4, 0, 22, 3, 5, 1]
    add 18-19  certificate [18, 3, 4, 0, 19, 5, 6, 1]
    add 18-20  certificate [18, 3, 4, 0, 20, 1, 5, 2]
    add 18-21  certificate [18, 3, 4, 0, 21, 2, 5, 1]
    add 18-22  certificate [18, 3, 4, 0, 22, 5, 6, 1]
    add 19-20  certificate [19, 0, 4, 1, 20, 5, 6, 2]
    add 21-22  certificate [21, 2, 4, 0, 22, 3, 5, 1]
    add 0-12  certificate [0, 1, 2, 3, 12, 4, 5, 6]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-16  certificate [0, 1, 2, 3, 16, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 0-18  certificate [0, 1, 2, 3, 18, 4, 5, 6]
    add 0-20  certificate [0, 1, 2, 3, 20, 4, 5, 6]
    add 0-21  certificate [0, 1, 2, 3, 21, 4, 5, 6]
    add 0-22  certificate [0, 1, 2, 3, 22, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 1-13  certificate [1, 0, 2, 3, 13, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-17  certificate [1, 0, 2, 3, 17, 4, 5, 6]
    add 1-18  certificate [1, 0, 2, 3, 18, 4, 5, 6]
    add 1-19  certificate [1, 0, 2, 3, 19, 4, 5, 6]
    add 1-21  certificate [1, 0, 2, 3, 21, 4, 5, 6]
    add 1-22  certificate [1, 0, 2, 3, 22, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-14  certificate [2, 0, 1, 3, 14, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 2-18  certificate [2, 0, 1, 3, 18, 4, 5, 6]
    add 2-19  certificate [2, 0, 1, 3, 19, 4, 5, 6]
    add 2-20  certificate [2, 0, 1, 3, 20, 4, 5, 6]
    add 2-22  certificate [2, 0, 1, 3, 22, 4, 5, 6]
    add 3-11  certificate [3, 0, 1, 2, 11, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-15  certificate [3, 0, 1, 2, 15, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
    add 3-17  certificate [3, 0, 1, 2, 17, 4, 5, 6]
    add 3-19  certificate [3, 0, 1, 2, 19, 4, 5, 6]
    add 3-20  certificate [3, 0, 1, 2, 20, 4, 5, 6]
    add 3-21  certificate [3, 0, 1, 2, 21, 4, 5, 6]
composite n=24: S_12 + 3 gadget(s) at 0,1,2,3; 42 edges; 234 steps
    add 0-1  certificate [0, 2, 4, 6, 1, 3, 5, 7]
    add 2-8  certificate [2, 3, 6, 7, 8, 1, 4, 5]
    add 7-8  certificate [7, 3, 5, 1, 8, 2, 4, 0]
    add 0-7  certificate [0, 1, 2, 8, 7, 5, 6, 4]
    add 1-6  certificate [1, 0, 3, 2, 6, 4, 7, 8]
    add 2-4  certificate [2, 0, 6, 7, 4, 10, 9, 11]
    add 2-5  certificate [2, 0, 3, 1, 5, 4, 7, 6]
    add 3-4  certificate [3, 1, 2, 0, 4, 5, 6, 7]
    add 3-6  certificate [3, 2, 7, 0, 6, 4, 11, 10]
    add 3-9  certificate [3, 2, 7, 0, 9, 4, 11, 10]
    add 3-10  certificate [3, 1, 9, 6, 10, 0, 4, 2]
    add 3-11  certificate [3, 4, 6, 2, 11, 10, 7, 0]
    add 4-7  certificate [4, 2, 6, 3, 7, 0, 11, 10]
    add 4-11  certificate [4, 0, 3, 1, 11, 7, 9, 6]
    add 5-6  certificate [5, 1, 2, 0, 6, 3, 4, 7]
    add 5-8  certificate [5, 2, 6, 3, 8, 4, 7, 11]
    add 5-9  certificate [5, 1, 2, 0, 9, 3, 4, 7]
    add 5-10  certificate [5, 1, 2, 0, 10, 3, 4, 7]
    add 5-11  certificate [5, 1, 2, 0, 11, 3, 4, 7]
    add 6-8  certificate [6, 1, 2, 0, 8, 5, 4, 7]
    add 6-10  certificate [6, 1, 2, 0, 10, 3, 4, 7]
    add 7-9  certificate [7, 0, 3, 1, 9, 4, 6, 5]
    add 7-10  certificate [7, 0, 3, 1, 10, 4, 6, 5]
    add 8-9  certificate [8, 1, 2, 0, 9, 3, 4, 7]
    add 8-10  certificate [8, 1, 2, 0, 10, 3, 4, 7]
    add 8-11  certificate [8, 1, 2, 0, 11, 3, 4, 7]
    add 9-10  certificate [9, 3, 4, 2, 10, 6, 5, 8]
    add 0-3  certificate [0, 1, 2, 5, 3, 6, 4, 7]
    add 0-5  certificate [0, 1, 2, 3, 5, 6, 4, 7]
    add 0-6  certificate [0, 1, 2, 3, 6, 5, 4, 7]
    add 0-8  certificate [0, 1, 2, 3, 8, 5, 4, 6]
    add 0-9  certificate [0, 1, 2, 3, 9, 5, 4, 6]
    add 0-11  certificate [0, 1, 2, 3, 11, 5, 4, 6]
    add 1-2  certificate [1, 0, 3, 4, 2, 5, 6, 7]
    add 1-4  certificate [1, 0, 2, 3, 4, 5, 6, 7]
    add 1-7  certificate [1, 0, 2, 3, 7, 4, 5, 6]
    add 1-9  certificate [1, 0, 2, 3, 9, 4, 5, 6]
    add 1-10  certificate [1, 0, 2, 3, 10, 4, 5, 6]
    add 1-11  certificate [1, 0, 2, 3, 11, 4, 5, 6]
    add 2-7  certificate [2, 0, 1, 3, 7, 4, 5, 6]
    add 2-9  certificate [2, 0, 1, 3, 9, 4, 5, 6]
    add 2-10  certificate [2, 0, 1, 3, 10, 4, 5, 6]
    add 2-11  certificate [2, 0, 1, 3, 11, 4, 5, 6]
    add 3-5  certificate [3, 0, 1, 2, 5, 4, 6, 7]
    add 3-8  certificate [3, 0, 1, 2, 8, 4, 5, 6]
    add 12-15  certificate [12, 0, 14, 2, 15, 3, 13, 1]
    add 16-19  certificate [16, 0, 18, 2, 19, 3, 17, 1]
    add 20-23  certificate [20, 0, 22, 2, 23, 3, 21, 1]
    add 4-12  certificate [4, 2, 3, 1, 12, 14, 15, 13]
    add 4-13  certificate [4, 2, 3, 0, 13, 14, 15, 12]
    add 4-14  certificate [4, 0, 1, 3, 14, 12, 13, 15]
    add 4-15  certificate [4, 0, 1, 2, 15, 12, 13, 14]
    add 4-16  certificate [4, 2, 3, 1, 16, 18, 19, 17]
    add 4-17  certificate [4, 2, 3, 0, 17, 18, 19, 16]
    add 4-18  certificate [4, 0, 1, 3, 18, 16, 17, 19]
    add 4-19  certificate [4, 0, 1, 2, 19, 16, 17, 18]
    add 4-20  certificate [4, 2, 3, 1, 20, 22, 23, 21]
    add 4-21  certificate [4, 2, 3, 0, 21, 22, 23, 20]
    add 4-22  certificate [4, 0, 1, 3, 22, 20, 21, 23]
    add 4-23  certificate [4, 0, 1, 2, 23, 20, 21, 22]
    add 5-12  certificate [5, 0, 2, 1, 12, 4, 14, 13]
    add 5-13  certificate [5, 0, 2, 3, 13, 1, 4, 6]
    add 5-14  certificate [5, 0, 1, 2, 14, 12, 13, 4]
    add 5-15  certificate [5, 0, 1, 2, 15, 3, 4, 6]
    add 5-16  certificate [5, 0, 2, 1, 16, 4, 18, 17]
    add 5-17  certificate [5, 0, 2, 3, 17, 1, 4, 6]
    add 5-18  certificate [5, 0, 1, 2, 18, 16, 17, 4]
    add 5-19  certificate [5, 0, 1, 2, 19, 3, 4, 6]
    add 5-20  certificate [5, 0, 2, 1, 20, 4, 22, 21]
    add 5-21  certificate [5, 0, 2, 3, 21, 1, 4, 6]
    add 5-22  certificate [5, 0, 1, 2, 22, 20, 21, 4]
    add 5-23  certificate [5, 0, 1, 2, 23, 3, 4, 6]
    add 6-12  certificate [6, 0, 1, 2, 12, 4, 5, 3]
    add 6-13  certificate [6, 0, 1, 2, 13, 4, 5, 3]
    add 6-14  certificate [6, 0, 1, 2, 14, 4, 5, 3]
    add 6-15  certificate [6, 0, 1, 2, 15, 3, 4, 5]
    add 6-16  certificate [6, 0, 1, 2, 16, 4, 5, 3]
    add 6-17  certificate [6, 0, 1, 2, 17, 4, 5, 3]
    add 6-18  certificate [6, 0, 1, 2, 18, 4, 5, 3]
    add 6-19  certificate [6, 0, 1, 2, 19, 3, 4, 5]
    add 6-20  certificate [6, 0, 1, 2, 20, 4, 5, 3]
    add 6-21  certificate [6, 0, 1, 2, 21, 4, 5, 3]
    add 6-22  certificate [6, 0, 1, 2, 22, 4, 5, 3]
    add 6-23  certificate [6, 0, 1, 2, 23, 3, 4, 5]
    add 7-12  certificate [7, 0, 1, 2, 12, 4, 5, 3]
    add 7-13  certificate [7, 0, 1, 2, 13, 4, 5, 3]
    add 7-14  certificate [7, 0, 1, 2, 14, 4, 5, 3]
    add 7-15  certificate [7, 0, 1, 2, 15, 3, 4, 5]
    add 7-16  certificate [7, 0, 1, 2, 16, 4, 5, 3]
    add 7-17  certificate [7, 0, 1, 2, 17, 4, 5, 3]
    add 7-18  certificate [7, 0, 1, 2, 18, 4, 5, 3]
    add 7-19  certificate [7, 0, 1, 2, 19, 3, 4, 5]
    add 7-20  certificate [7, 0, 1, 2, 20, 4, 5, 3]
    add 7-21  certificate [7, 0, 1, 2, 21, 4, 5, 3]
    add 7-22  certificate [7, 0, 1, 2, 22, 4, 5, 3]
    add 7-23  certificate [7, 0, 1, 2, 23, 3, 4, 5]
    add 8-12  certificate [8, 0, 1, 2, 12, 4, 5, 3]
    add 8-13  certificate [8, 0, 1, 2, 13, 4, 5, 3]
    add 8-14  certificate [8, 0, 1, 2, 14, 4, 5, 3]
    add 8-15  certificate [8, 0, 1, 2, 15, 3, 4, 5]
    add 8-16  certificate [8, 0, 1, 2, 16, 4, 5, 3]
    add 8-17  certificate [8, 0, 1, 2, 17, 4, 5, 3]
    add 8-18  certificate [8, 0, 1, 2, 18, 4, 5, 3]
    add 8-19  certificate [8, 0, 1, 2, 19, 3, 4, 5]
    add 8-20  certificate [8, 0, 1, 2, 20, 4, 5, 3]
    add 8-21  certificate [8, 0, 1, 2, 21, 4, 5, 3]
    add 8-22  certificate [8, 0, 1, 2, 22, 4, 5, 3]
    add 8-23  certificate [8, 0, 1, 2, 23, 3, 4, 5]
    add 9-12  certificate [9, 0, 1, 2, 12, 4, 5, 3]
    add 9-13  certificate [9, 0, 1, 2, 13, 4, 5, 3]
    add 9-14  certificate [9, 0, 1, 2, 14, 4, 5, 3]
    add 9-15  certificate [9, 0, 1, 2, 15, 3, 4, 5]
    add 9-16  certificate [9, 0, 1, 2, 16, 4, 5, 3]
    add 9-17  certificate [9, 0, 1, 2, 17, 4, 5, 3]
    add 9-18  certificate [9, 0, 1, 2, 18, 4, 5, 3]
    add 9-19  certificate [9, 0, 1, 2, 19, 3, 4, 5]
    add 9-20  certificate [9, 0, 1, 2, 20, 4, 5, 3]
    add 9-21  certificate [9, 0, 1, 2, 21, 4, 5, 3]
    add 9-22  certificate [9, 0, 1, 2, 22, 4, 5, 3]
    add 9-23  certificate [9, 0, 1, 2, 23, 3, 4, 5]
    add 10-12  certificate [10, 0, 1, 2, 12, 4, 5, 3]
    add 10-13  certificate [10, 0, 1, 2, 13, 4, 5, 3]
    add 10-14  certificate [10, 0, 1, 2, 14, 4, 5, 3]
    add 10-15  certificate [10, 0, 1, 2, 15, 3, 4, 5]
    add 10-16  certificate [10, 0, 1, 2, 16, 4, 5, 3]
    add 10-17  certificate [10, 0, 1, 2, 17, 4, 5, 3]
    add 10-18  certificate [10, 0, 1, 2, 18, 4, 5, 3]
    add 10-19  certificate [10, 0, 1, 2, 19, 3, 4, 5]
    add 10-20  certificate [10, 0, 1, 2, 20, 4, 5, 3]
    add 10-21  certificate [10, 0, 1, 2, 21, 4, 5, 3]
    add 10-22  certificate [10, 0, 1, 2, 22, 4, 5, 3]
    add 10-23  certificate [10, 0, 1, 2, 23, 3, 4, 5]
    add 11-12  certificate [11, 0, 1, 2, 12, 4, 5, 3]
    add 11-13  certificate [11, 0, 1, 2, 13, 4, 5, 3]
    add 11-14  certificate [11, 0, 1, 2, 14, 4, 5, 3]
    add 11-15  certificate [11, 0, 1, 2, 15, 3, 4, 5]
    add 11-16  certificate [11, 0, 1, 2, 16, 4, 5, 3]
    add 11-17  certificate [11, 0, 1, 2, 17, 4, 5, 3]
    add 11-18  certificate [11, 0, 1, 2, 18, 4, 5, 3]
    add 11-19  certificate [11, 0, 1, 2, 19, 3, 4, 5]
    add 11-20  certificate [11, 0, 1, 2, 20, 4, 5, 3]
    add 11-21  certificate [11, 0, 1, 2, 21, 4, 5, 3]
    add 11-22  certificate [11, 0, 1, 2, 22, 4, 5, 3]
    add 11-23  certificate [11, 0, 1, 2, 23, 3, 4, 5]
    add 12-13  certificate [12, 0, 4, 1, 13, 5, 6, 2]
    add 12-16  certificate [12, 0, 4, 1, 16, 5, 6, 2]
    add 12-17  certificate [12, 0, 4, 1, 17, 5, 6, 2]
    add 12-18  certificate [12, 0, 4, 1, 18, 2, 5, 3]
    add 12-19  certificate [12, 0, 4, 1, 19, 3, 5, 2]
    add 12-20  certificate [12, 0, 4, 1, 20, 5, 6, 2]
    add 12-21  certificate [12, 0, 4, 1, 21, 5, 6, 2]
    add 12-22  certificate [12, 0, 4, 1, 22, 2, 5, 3]
    add 12-23  certificate [12, 0, 4, 1, 23, 3, 5, 2]
    add 13-16  certificate [13, 1, 4, 0, 16, 5, 6, 2]
    add 13-17  certificate [13, 1, 4, 0, 17, 5, 6, 2]
    add 13-18  certificate [13, 1, 4, 0, 18, 2, 5, 3]
    add 13-19  certificate [13, 1, 4, 0, 19, 3, 5, 2]
    add 13-20  certificate [13, 1, 4, 0, 20, 5, 6, 2]
    add 13-21  certificate [13, 1, 4, 0, 21, 5, 6, 2]
    add 13-22  certificate [13, 1, 4, 0, 22, 2, 5, 3]
    add 13-23  certificate [13, 1, 4, 0, 23, 3, 5, 2]
    add 14-15  certificate [14, 2, 4, 0, 15, 3, 5, 1]
    add 14-16  certificate [14, 2, 4, 0, 16, 5, 6, 1]
    add 14-17  certificate [14, 2, 4, 0, 17, 1, 5, 3]
    add 14-18  certificate [14, 2, 4, 0, 18, 5, 6, 1]
    add 14-19  certificate [14, 2, 4, 0, 19, 3, 5, 1]
    add 14-20  certificate [14, 2, 4, 0, 20, 5, 6, 1]
    add 14-21  certificate [14, 2, 4, 0, 21, 1, 5, 3]
    add 14-22  certificate [14, 2, 4, 0, 22, 5, 6, 1]
    add 14-23  certificate [14, 2, 4, 0, 23, 3, 5, 1]
    add 15-16  certificate [15, 3, 4, 0, 16, 5, 6, 1]
    add 15-17  certificate [15, 3, 4, 0, 17, 1, 5, 2]
    add 15-18  certificate [15, 3, 4, 0, 18, 2, 5, 1]
    add 15-19  certificate [15, 3, 4, 0, 19, 5, 6, 1]
    add 15-20  certificate [15, 3, 4, 0, 20, 5, 6, 1]
    add 15-21  certificate [15, 3, 4, 0, 21, 1, 5, 2]
    add 15-22  certificate [15, 3, 4, 0, 22, 2, 5, 1]
    add 15-23  certificate [15, 3, 4, 0, 23, 5, 6, 1]
    add 16-17  certificate [16, 0, 4, 1, 17, 5, 6, 2]
    add 16-20  certificate [16, 0, 4, 1, 20, 5, 6, 2]
    add 16-21  certificate [16, 0, 4, 1, 21, 5, 6, 2]
    add 16-22  certificate [16, 0, 4, 1, 22, 2, 5, 3]
    add 16-23  certificate [16, 0, 4, 1, 23, 3, 5, 2]
    add 17-20  certificate [17, 1, 4, 0, 20, 5, 6, 2]
    add 17-21  certificate [17, 1, 4, 0, 21, 5, 6, 2]
    add 17-22  certificate [17, 1, 4, 0, 22, 2, 5, 3]
    add 17-23  certificate [17, 1, 4, 0, 23, 3, 5, 2]
    add 18-19  certificate [18, 2, 4, 0, 19, 3, 5, 1]
    add 18-20  certificate [18, 2, 4, 0, 20, 5, 6, 1]
    add 18-21  certificate [18, 2, 4, 0, 21, 1, 5, 3]
    add 18-22  certificate [18, 2, 4, 0, 22, 5, 6, 1]
    add 18-23  certificate [18, 2, 4, 0, 23, 3, 5, 1]
    add 19-20  certificate [19, 3, 4, 0, 20, 5, 6, 1]
    add 19-21  certificate [19, 3, 4, 0, 21, 1, 5, 2]
    add 19-22  certificate [19, 3, 4, 0, 22, 2, 5, 1]
    add 19-23  certificate [19, 3, 4, 0, 23, 5, 6, 1]
    add 20-21  certificate [20, 0, 4, 1, 21, 5, 6, 2]
    add 22-23  certificate [22, 2, 4, 0, 23, 3, 5, 1]
    add 0-13  certificate [0, 1, 2, 3, 13, 4, 5, 6]
    add 0-14  certificate [0, 1, 2, 3, 14, 4, 5, 6]
    add 0-15  certificate [0, 1, 2, 3, 15, 4, 5, 6]
    add 0-17  certificate [0, 1, 2, 3, 17, 4, 5, 6]
    add 0-18  certificate [0, 1, 2, 3, 18, 4, 5, 6]
    add 0-19  certificate [0, 1, 2, 3, 19, 4, 5, 6]
    add 0-21  certificate [0, 1, 2, 3, 21, 4, 5, 6]
    add 0-22  certificate [0, 1, 2, 3, 22, 4, 5, 6]
    add 0-23  certificate [0, 1, 2, 3, 23, 4, 5, 6]
    add 1-12  certificate [1, 0, 2, 3, 12, 4, 5, 6]
    add 1-14  certificate [1, 0, 2, 3, 14, 4, 5, 6]
    add 1-15  certificate [1, 0, 2, 3, 15, 4, 5, 6]
    add 1-16  certificate [1, 0, 2, 3, 16, 4, 5, 6]
    add 1-18  certificate [1, 0, 2, 3, 18, 4, 5, 6]
    add 1-19  certificate [1, 0, 2, 3, 19, 4, 5, 6]
    add 1-20  certificate [1, 0, 2, 3, 20, 4, 5, 6]
    add 1-22  certificate [1, 0, 2, 3, 22, 4, 5, 6]
    add 1-23  certificate [1, 0, 2, 3, 23, 4, 5, 6]
    add 2-12  certificate [2, 0, 1, 3, 12, 4, 5, 6]
    add 2-13  certificate [2, 0, 1, 3, 13, 4, 5, 6]
    add 2-15  certificate [2, 0, 1, 3, 15, 4, 5, 6]
    add 2-16  certificate [2, 0, 1, 3, 16, 4, 5, 6]
    add 2-17  certificate [2, 0, 1, 3, 17, 4, 5, 6]
    add 2-19  certificate [2, 0, 1, 3, 19, 4, 5, 6]
    add 2-20  certificate [2, 0, 1, 3, 20, 4, 5, 6]
    add 2-21  certificate [2, 0, 1, 3, 21, 4, 5, 6]
    add 2-23  certificate [2, 0, 1, 3, 23, 4, 5, 6]
    add 3-12  certificate [3, 0, 1, 2, 12, 4, 5, 6]
    add 3-13  certificate [3, 0, 1, 2, 13, 4, 5, 6]
    add 3-14  certificate [3, 0, 1, 2, 14, 4, 5, 6]
    add 3-16  certificate [3, 0, 1, 2, 16, 4, 5, 6]
    add 3-17  certificate [3, 0, 1, 2, 17, 4, 5, 6]
    add 3-18  certificate [3, 0, 1, 2, 18, 4, 5, 6]
    add 3-20  certificate [3, 0, 1, 2, 20, 4, 5, 6]
    add 3-21  certificate [3, 0, 1, 2, 21, 4, 5, 6]
    add 3-22  certificate [3, 0, 1, 2, 22, 4, 5, 6]
ok    graphs with gadgets, 13 <= n <= 24: percolate with floor((7n+2)/4) edges, every step certified
ok    Proposition 5.1 / controls: n=8 k=3: 560 sets with (R1), 0 work
ok    Proposition 5.1 / controls: n=8 k=4: 1820 sets with (R1), 768 work
ok    Proposition 5.1 / controls: n=9 k=4: 4326 sets with (R1), 0 work
ok    Proposition 5.1 / controls: n=9 k=5: 23576 sets with (R1), 6864 work
ALL CHECKS PASSED
