C Count lacings of a shoe with two rows of N eyelets
C subjected to the "physical" condition that all
C eyelets are "loaded", i.e. that there is a force
C component towards the opposite eyelet column.
C
C Author: Hugo Pfoertner http:/www.pfoertner.org/
C
C Version history:
C 05.01.2003 NEXPER replaced by LPG
C 03.01.2003 Count crossing-free lacings (OEIS sequence A079410)
C 17.12.2002 Initial version
C
C N is the number of eyelets in one row.
C N=8 takes approx 1day CPU time on an Intel PIII 550MHz,
C ((2*8-2)!=14! configs to check)
C N=9 is expected to run approx 15*16=240days on the same CPU.
C
PARAMETER (N=4, N2=N+N, M=N2-2, N2P=N2+1, N2M=N2-1)
PARAMETER (NN=N*N+N*N)
PARAMETER ( EPS0=0.001D0, EPS1=0.999D0)
INTEGER E(N2), EE(N,2), A(M), CC(0:NN)
INTEGER LOVER
DOUBLEPRECISION Q
EQUIVALENCE (E,EE)
C
C FIXED START AND END
EE(1,1) = 1
EE(N,2) = N2
C PRESET PERMUTATION ARRAY
DO 2 I = 1, M
A(I) = I
2 CONTINUE
C STATUS OF PERMUTATION GENERATION
NEXT = -1
C CONTER FOR LEGAL LACINGS
L = 0
C OVERFLOW COUNTER IF L EXCEEDS 1E9
C THIS OCCURS FOR N>=8
C TOTAL COUNT: LOVER*1E9 + L
LOVER = 0
C COUNTER FOR CROSSINGS
DO 5 I = 0, NN
CC(I) = 0
5 CONTINUE
C
WRITE (*,1002) N
1002 FORMAT ( ' N =', I2, // , 'Crossing-free Lacings:', / )
C
10 CONTINUE
C CREATE NEXT PERMUTATION
IF ( NEXT .EQ. -1 ) THEN
NEXT = 1
ELSE
C Create permutations in lexicographic order
CALL LPG ( M, A, NEXT )
ENDIF
IF ( NEXT .EQ. 0 ) GOTO 200
C INSERT PERMUTED PATH BETWEEN FIXED START AND END
DO 20 I = 1, M
E(I+1) = A(I) + 1
20 CONTINUE
C TEST CONDITION THAT AT LEAST ONE OF THE DIRECTLY CONNECTED
C EYELETS IS ON THE OPPOSITE SIDE
DO 30 I = 2, N2M
IF ( E(I) .LE. N ) THEN
IF ( E(I-1) .GT. N ) GOTO 30
IF ( E(I+1) .GT. N ) GOTO 30
ELSE
IF ( E(I-1) .LE. N ) GOTO 30
IF ( E(I+1) .LE. N ) GOTO 30
ENDIF
C UNLOADED EYELET FOUND, ABANDON PATH
GOTO 10
30 CONTINUE
C
C LEGAL LACING FOUND, CHECK FOR CROSSINGS
C Left eyelet row at x=0, right row at x=1,
C determine if intersection of lace path intervals
C occurs between x=eps0 and x=eps1
C (eps0=0.001, eps1=0.999)
C g1 given by two points (0,II),(1,JJ)
C g2 given by two points (0,KK),(1,LL)
C
C K counts crossings
K = 0
C
DO 40 I = 2, N2M
C IF BOTH ON SAME SIDE NO FURTHER CHECK NECESSARY
IF ( E(I-1) .LE. N ) THEN
C BOTH ON SAME SIDE, NO FURTHER CHECK
IF ( E(I) .LE. N ) GOTO 40
II = E(I-1)
JJ = N2P - E(I)
ELSE
C BOTH ON SAME SIDE, NO FURTHER CHECK
IF ( E(I) .GT. N ) GOTO 40
II = E(I)
JJ = N2P - E(I-1)
ENDIF
DO 50 J = I, N2M
IF ( E(J) .LE. N ) THEN
C BOTH ON SAME SIDE, NO FURTHER CHECK
IF ( E(J+1) .LE. N ) GOTO 50
KK = E(J)
LL = N2P - E(J+1)
ELSE
C BOTH ON SAME SIDE, NO FURTHER CHECK
IF ( E(J+1) .GT. N ) GOTO 50
KK = E(J+1)
LL = N2P - E(J)
ENDIF
C DIAGNOSTIC OUTPUT
C WRITE (*,*) II, JJ, KK, LL
NUM = II - KK
NEN = LL - JJ + NUM
IF ( NEN .EQ. 0 ) GOTO 50
Q = DBLE(NUM)/DBLE(NEN)
IF ( Q .LE. EPS0 ) GOTO 50
IF ( Q .GE. EPS1 ) GOTO 50
C INCREASE CROSS COUNT
K = K + 1
50 CONTINUE
40 CONTINUE
C COUNT LACINGS
L = L + 1
IF ( L .GT. 1000000000 ) THEN
L = L - 1000000000
LOVER = LOVER + 1
WRITE (*,*) ' L OVERFLOW: ', LOVER
ENDIF
C TO PRINT RESULTS ACTIVATE COMMENTED LINES
C PRINT CROSSING-FREE CONFIGS (deactivate for N=8)
IF ( K .EQ. 0 )
& WRITE (*,1000) L, K, (E(I),I=1,N2)
1000 FORMAT (I8, I2, 2I3,:,2I3,:,2I3,:,2I3,:,2I3,:,2I3,:,2I3,:,2I3)
C UPDATE CROSSING COUNT HISTOGRAM
CC(K) = CC(K) + 1
IF ( NEXT .EQ. 1 ) GOTO 10
C
200 CONTINUE
WRITE (*,*) ' LOVER=', LOVER, ' L=', L
WRITE (*,*) ' Crossings, #'
DO 100 I = 0, NN
IF ( CC(I) .GT. 0 ) WRITE (*,1001) I, CC(I)
1001 FORMAT ( I3, I10 )
100 CONTINUE
END
C********************************************************************
SUBROUTINE LPG ( N, A, NEXT )
C
C Generate next permutation of N elements A(i) in
C lexicographic order
C
C The method used is
C "Algorithm L (Lexicographic permutation generation)"
C described in Chapter 7.2.1.2
C with the modification proposed in the answer to
C exercise 1 [J.P.N. Phillips, Comp. J. 10 (1967), 311)]
C of Donald E. Knuth's The Art of Computer Programming, Volume 4,
C Combinatorial Algorithms, C Volume 4A, Enumeration and Backtracking.
C The printed book is expected to be available in the year 2007.
C D. Knuth has put some chapters online, including
C Pre-fascicle 2b (generating all permutations), available at
C http://www-cs-faculty.stanford.edu/~knuth/fasc2b.ps.gz
C Most of the comments are copied verbally from Knuth's
C description
C
C Author: Hugo Pfoertner http://www.pfoertner.org/
C
C Change history:
C 06.01.2003 Optional code to treat N<4
C 05.01.2003 Initial version
C
C Call parameters:
INTEGER N, A(N), NEXT
C N: number of elements to permute. N>=4 must hold (not checked)
C A: Integer array holding the elements.
C to be preset externally (e.g. by 1,2,3,...,n-1,n)
C A is overwritten by the lexicographically next permutation
C NEXT: =1 if A has been successfully updated
C =0 if A was already in reverse lexicographic order
C i.e. if a(n)>=a(n-1)>=....>=a(2)>=a(1)
C In this case no change is made to A
C
C Local variables
INTEGER J, K, L, X, Y, Z, H
C
C Preset return status
NEXT = 1
C
C In a generally applicable version for all N all lines starting
C with comment CS have to be activated
CSC Start part necessary for N<3
CS IF ( N .LE. 1 ) THEN
CS NEXT = 0
CS RETURN
CS ENDIF
CS IF ( N .EQ. 2 ) THEN
CS IF ( A(1) .LT. A(2) ) THEN
CS H = A(1)
CS A(1) = A(2)
CS A(2) = H
CS ELSE
CS NEXT = 0
CS ENDIF
CS RETURN
CS ENDIF
CSC End part necessary for N<3
C
C Find the largest j such that a(j) can be increased
C
C Step L2 finds j=n-1 half of the time when the elements are distinct,
C because exactly n!/2 of the n! permutations have a(n-1)= a(l) decrease l repeatedly until a(j)a(l)
C
C L3' Easy increase?
IF ( Y .LT. Z ) THEN
A(J) = Z
A(J+1) = Y
A(N) = X
C Done, go to L4.1'
GOTO 41
ENDIF
C L3.1' Increase A(J)
L = N - 1
20 CONTINUE
IF ( Y .GE. A(L) ) THEN
L = L - 1
GOTO 20
ENDIF
C
C Since a(j+1) >= ... >= a(n), element a(l) is the smallest element
C greater than a(j) that can legitimately follow a(1)...a(j-1) in a
C permutation. Before the interchange we have a(j+1)>=...>=a(l-1)>=a(l)
C >a(j)>=a(l+1)>=...>=a(n)
C
C Interchange
C
A(J) = A(L)
A(L) = Y
C
C After the interchange, we have
C a(j+1)>=...>=a(l-1)>=a(j)>a(l)>=a(l+1)>=...>=a(n)
C
C Find the lexicographically least way to extend the new a(1)...a(j)
C to a complete pattern:
C The first permutation beginning with the current prefix a(1)...a(j)
C is a(1)...a(j)a(n)...a(j+1), and step L4 produces it by doing
C floor (n-j)/2 interchanges
C
C L4 Reverse a(j+1)...a(n)
C L4' Begin to reverse
A(N) = A(J+1)
A(J+1) = Z
C L4.1' Reverse a(j+1)...a(n-1)
41 CONTINUE
K = J + 2
L = N - 1
30 CONTINUE
IF ( K .LT. L ) THEN
H = A(K)
A(K) = A(L)
A(L) = H
K = K + 1
L = L - 1
GOTO 30
ENDIF
RETURN
C End of SUBROUTINE LPG
END
---------------------------------------------------------------------
Results, edited + some ASCII illustrations
N = 3
Crossing-free Lacings:
3 0 1 2 5 3 4 6
5 0 1 3 4 2 5 6
6 0 1 3 4 5 2 6
15 0 1 5 2 3 4 6
L= 20 (=A078698(n))
3 5 6 15
1 6 1 6 1 6 1 6
| | | | | / \ |
| | | | | / \ |
| | | | | / \ |
2___5| |2___5 |2___5 2___5|
/ | | \ | | | |
/ | | \ | | | |
/ | | \ | | | |
3____4 3____4 3____4 3____4
Crossings, #
0 4 =2*A079410(3)
1 7
2 5
3 3
6 1 (6=A000384(2))
---------------------------------------------------------------------
N = 4
Crossing-free Lacings:
35 0 1 2 7 3 6 4 5 8
43 0 1 2 7 5 4 3 6 8
45 0 1 2 7 6 3 4 5 8
70 0 1 3 6 4 5 7 2 8
75 0 1 3 6 5 4 2 7 8
77 0 1 3 6 7 2 4 5 8
101 0 1 4 5 3 6 2 7 8
102 0 1 4 5 3 6 7 2 8
107 0 1 4 5 6 3 2 7 8
108 0 1 4 5 6 3 7 2 8
109 0 1 4 5 7 2 3 6 8
315 0 1 7 2 3 6 4 5 8
317 0 1 7 2 4 5 3 6 8
327 0 1 7 2 6 3 4 5 8
L= 396
35 43 45 70 77 102 108
1 8 1 8 1 8 1 8 1 8 1 8 1 8
| | | | | | | / | | | / | /
| | | | | | | / | | | / | /
| | | | | | | / | | | / | /
2___7| 2___7| 2___7| |2___7 |2__7| |2___7 |2___7
/ | \/ || | | \/ || | | | /
/ | /\ || | | /\ || | | | /
/ | || || | | || || | | | /
3___6| 3___6| 3___6| 3___6| |3__6| |3___6 |3___6
/ | | | | | / | | | | \ | |
/ | | | | | / | | | | \ | |
/ | | | | | / | | | | \ | |
4____5 4____5 4____5 4____5 4____5 4____5 4____5
109 75 107 317 109 315 327
1 8 1 8 1 8 1 8 1 8 1 8 1 8
| | | | | | \ | | | \ | \ |
| | | | | | \ | | | \ | \ |
| | | | | | \ | | | \ | \ |
|2___7 |2___7 |2___7 2___7| |2__7| 2___7| 2___7|
| \ \/ || | | || \/ | | \ |
| \ /\ || | | || /\ | | \ |
| \ || || | | || || | | \ |
|3___6 |3___6 |3___6 |3___6 |3__6| 3___6| 3___6|
| \ | | | | | \ | | / | | |
| \ | | | | | \ | | / | | |
| \ | | | | | \ | | / | | |
4____5 4____5 4____5 4____5 4____5 4____5 4____5
Crossings, #
0 14 =2*A079410(4)
1 36
2 51
3 69
4 84
5 52
6 34
7 29
8 13
9 6
11 3
12 4
15 1 (15=A000384(3))
--------------------------------------------------------------------
N = 5
Crossing-free Lacings:
1085 0 1 2 9 3 4 8 6 5 7 10
1086 0 1 2 9 3 4 8 7 5 6 10
1087 0 1 2 9 3 5 6 7 4 8 10
1088 0 1 2 9 3 5 6 8 4 7 10
1127 0 1 2 9 3 8 4 7 5 6 10
1135 0 1 2 9 3 8 6 5 4 7 10
1137 0 1 2 9 3 8 7 4 5 6 10
1303 0 1 2 9 6 5 3 8 4 7 10
1305 0 1 2 9 6 5 4 7 3 8 10
1311 0 1 2 9 6 5 7 4 3 8 10
1351 0 1 2 9 7 4 6 5 3 8 10
1355 0 1 2 9 7 4 8 3 5 6 10
1383 0 1 2 9 8 3 4 7 5 6 10
1385 0 1 2 9 8 3 5 6 4 7 10
1395 0 1 2 9 8 3 7 4 5 6 10
1867 0 1 3 7 4 5 6 8 2 9 10
1868 0 1 3 7 4 5 6 9 2 8 10
2215 0 1 3 8 2 9 6 5 4 7 10
2217 0 1 3 8 2 9 7 4 5 6 10
2225 0 1 3 8 4 2 9 6 5 7 10
2226 0 1 3 8 4 2 9 7 5 6 10
2254 0 1 3 8 4 7 5 6 9 2 10
2259 0 1 3 8 4 7 6 5 2 9 10
2261 0 1 3 8 4 7 9 2 5 6 10
2386 0 1 3 8 6 5 4 7 9 2 10
2391 0 1 3 8 6 5 7 4 2 9 10
2426 0 1 3 8 7 4 5 6 9 2 10
2431 0 1 3 8 7 4 6 5 2 9 10
2463 0 1 3 8 9 2 4 7 5 6 10
2465 0 1 3 8 9 2 5 6 4 7 10
2525 0 1 3 9 2 4 8 6 5 7 10
2526 0 1 3 9 2 4 8 7 5 6 10
2527 0 1 3 9 2 5 6 7 4 8 10
2528 0 1 3 9 2 5 6 8 4 7 10
2754 0 1 3 9 6 5 7 8 4 2 10
2800 0 1 3 9 7 4 8 6 5 2 10
2814 0 1 3 9 7 5 6 8 4 2 10
2860 0 1 3 9 8 4 7 6 5 2 10
3005 0 1 4 6 5 2 9 7 3 8 10
3006 0 1 4 6 5 2 9 8 3 7 10
3007 0 1 4 6 5 3 7 8 2 9 10
3008 0 1 4 6 5 3 7 9 2 8 10
3307 0 1 4 7 3 5 6 8 2 9 10
3308 0 1 4 7 3 5 6 9 2 8 10
3339 0 1 4 7 3 8 6 5 2 9 10
3341 0 1 4 7 3 8 9 2 5 6 10
3383 0 1 4 7 5 6 8 3 2 9 10
3384 0 1 4 7 5 6 8 3 9 2 10
3385 0 1 4 7 5 6 9 2 3 8 10
3463 0 1 4 7 6 5 2 9 3 8 10
3465 0 1 4 7 6 5 3 8 2 9 10
3466 0 1 4 7 6 5 3 8 9 2 10
3506 0 1 4 7 8 3 5 6 9 2 10
3515 0 1 4 7 8 3 9 2 5 6 10
3520 0 1 4 7 8 3 9 6 5 2 10
3555 0 1 4 7 9 2 8 3 5 6 10
3580 0 1 4 7 9 3 8 6 5 2 10
3665 0 1 4 8 3 2 9 6 5 7 10
3666 0 1 4 8 3 2 9 7 5 6 10
3834 0 1 4 8 6 5 7 9 3 2 10
3894 0 1 4 8 7 5 6 9 3 2 10
4445 0 1 5 6 4 2 9 7 3 8 10
4446 0 1 5 6 4 2 9 8 3 7 10
4447 0 1 5 6 4 3 7 8 2 9 10
4448 0 1 5 6 4 3 7 9 2 8 10
4457 0 1 5 6 4 7 3 8 2 9 10
4458 0 1 5 6 4 7 3 8 9 2 10
4463 0 1 5 6 4 7 8 3 2 9 10
4464 0 1 5 6 4 7 8 3 9 2 10
4465 0 1 5 6 4 7 9 2 3 8 10
4543 0 1 5 6 7 4 2 9 3 8 10
4545 0 1 5 6 7 4 3 8 2 9 10
4546 0 1 5 6 7 4 3 8 9 2 10
4551 0 1 5 6 7 4 8 3 2 9 10
4552 0 1 5 6 7 4 8 3 9 2 10
4554 0 1 5 6 7 4 8 9 3 2 10
4586 0 1 5 6 8 3 4 7 9 2 10
4591 0 1 5 6 8 3 7 4 2 9 10
4595 0 1 5 6 8 3 9 2 4 7 10
4600 0 1 5 6 8 3 9 7 4 2 10
4614 0 1 5 6 8 4 7 9 3 2 10
4623 0 1 5 6 9 2 3 8 4 7 10
4625 0 1 5 6 9 2 4 7 3 8 10
4635 0 1 5 6 9 2 8 3 4 7 10
4660 0 1 5 6 9 3 8 7 4 2 10
12707 0 1 9 2 3 8 4 7 5 6 10
12715 0 1 9 2 3 8 6 5 4 7 10
12717 0 1 9 2 3 8 7 4 5 6 10
12747 0 1 9 2 4 7 6 5 3 8 10
12749 0 1 9 2 4 7 8 3 5 6 10
12773 0 1 9 2 5 6 4 7 3 8 10
12779 0 1 9 2 5 6 7 4 3 8 10
12781 0 1 9 2 5 6 8 3 4 7 10
12987 0 1 9 2 8 3 4 7 5 6 10
12989 0 1 9 2 8 3 5 6 4 7 10
12999 0 1 9 2 8 3 7 4 5 6 10
14443 0 1 9 6 5 2 8 3 4 7 10
14451 0 1 9 6 5 3 7 4 2 8 10
14455 0 1 9 6 5 3 8 2 4 7 10
14463 0 1 9 6 5 4 7 3 2 8 10
14571 0 1 9 7 3 4 6 5 2 8 10
14583 0 1 9 7 3 5 6 4 2 8 10
14623 0 1 9 7 4 2 8 3 5 6 10
14635 0 1 9 7 4 3 8 2 5 6 10
14743 0 1 9 8 2 3 7 4 5 6 10
14751 0 1 9 8 2 4 6 5 3 7 10
14755 0 1 9 8 2 4 7 3 5 6 10
14763 0 1 9 8 2 5 6 4 3 7 10
L= 14976
Crossings, #
0 108 =2*A079410(5)
1 328
2 650
3 1035
4 1441
5 1602
6 1640
7 1505
8 1437
9 1332
10 1027
11 904
12 634
13 535
14 327
15 166
16 94
17 67
18 55
19 14
20 20
21 26
22 17
24 5
25 6
28 1 (28=A000384(4))
--------------------------------------------------------------------
N = 6
Crossing-free Lacings:
55409 0 1 2 11 3 4 10 5 9 7 6 8 12
55410 0 1 2 11 3 4 10 5 9 8 6 7 12
55421 0 1 2 11 3 4 10 7 6 8 5 9 12
55435 0 1 2 11 3 4 10 9 5 8 6 7 12
55483 0 1 2 11 3 5 8 6 7 9 4 10 12
55484 0 1 2 11 3 5 8 6 7 10 4 9 12
55517 0 1 2 11 3 5 9 4 10 7 6 8 12
55518 0 1 2 11 3 5 9 4 10 8 6 7 12
55591 0 1 2 11 3 6 7 5 8 9 4 10 12
55592 0 1 2 11 3 6 7 5 8 10 4 9 12
55601 0 1 2 11 3 6 7 8 5 9 4 10 12
55615 0 1 2 11 3 6 7 10 4 9 5 8 12
56813 0 1 2 11 3 10 4 5 9 7 6 8 12
56814 0 1 2 11 3 10 4 5 9 8 6 7 12
56815 0 1 2 11 3 10 4 6 7 8 5 9 12
56816 0 1 2 11 3 10 4 6 7 9 5 8 12
56855 0 1 2 11 3 10 4 9 5 8 6 7 12
56863 0 1 2 11 3 10 4 9 7 6 5 8 12
56865 0 1 2 11 3 10 4 9 8 5 6 7 12
57031 0 1 2 11 3 10 7 6 4 9 5 8 12
57033 0 1 2 11 3 10 7 6 5 8 4 9 12
57039 0 1 2 11 3 10 7 6 8 5 4 9 12
57079 0 1 2 11 3 10 8 5 7 6 4 9 12
57083 0 1 2 11 3 10 8 5 9 4 6 7 12
57111 0 1 2 11 3 10 9 4 5 8 6 7 12
57113 0 1 2 11 3 10 9 4 6 7 5 8 12
57123 0 1 2 11 3 10 9 4 8 5 6 7 12
64007 0 1 2 11 7 6 3 10 4 9 5 8 12
64015 0 1 2 11 7 6 3 10 8 5 4 9 12
64017 0 1 2 11 7 6 3 10 9 4 5 8 12
64047 0 1 2 11 7 6 4 9 8 5 3 10 12
64049 0 1 2 11 7 6 4 9 10 3 5 8 12
64073 0 1 2 11 7 6 5 8 4 9 3 10 12
64079 0 1 2 11 7 6 5 8 9 4 3 10 12
64081 0 1 2 11 7 6 5 8 10 3 4 9 12
64159 0 1 2 11 7 6 8 5 3 10 4 9 12
64161 0 1 2 11 7 6 8 5 4 9 3 10 12
64167 0 1 2 11 7 6 8 5 9 4 3 10 12
65203 0 1 2 11 8 5 3 10 7 6 4 9 12
65205 0 1 2 11 8 5 3 10 9 4 6 7 12
65235 0 1 2 11 8 5 4 9 7 6 3 10 12
65237 0 1 2 11 8 5 4 9 10 3 6 7 12
65267 0 1 2 11 8 5 6 7 9 4 3 10 12
65269 0 1 2 11 8 5 6 7 10 3 4 9 12
65347 0 1 2 11 8 5 7 6 3 10 4 9 12
65349 0 1 2 11 8 5 7 6 4 9 3 10 12
65423 0 1 2 11 8 5 9 4 10 3 6 7 12
66391 0 1 2 11 9 4 3 10 7 6 5 8 12
66393 0 1 2 11 9 4 3 10 8 5 6 7 12
66423 0 1 2 11 9 4 5 8 7 6 3 10 12
66425 0 1 2 11 9 4 5 8 10 3 6 7 12
66455 0 1 2 11 9 4 6 7 8 5 3 10 12
66457 0 1 2 11 9 4 6 7 10 3 5 8 12
66607 0 1 2 11 9 4 8 5 7 6 3 10 12
66663 0 1 2 11 9 4 10 3 5 8 6 7 12
66665 0 1 2 11 9 4 10 3 6 7 5 8 12
67571 0 1 2 11 10 3 4 9 5 8 6 7 12
67579 0 1 2 11 10 3 4 9 7 6 5 8 12
67581 0 1 2 11 10 3 4 9 8 5 6 7 12
67611 0 1 2 11 10 3 5 8 7 6 4 9 12
67613 0 1 2 11 10 3 5 8 9 4 6 7 12
67637 0 1 2 11 10 3 6 7 5 8 4 9 12
67643 0 1 2 11 10 3 6 7 8 5 4 9 12
67645 0 1 2 11 10 3 6 7 9 4 5 8 12
67851 0 1 2 11 10 3 9 4 5 8 6 7 12
67853 0 1 2 11 10 3 9 4 6 7 5 8 12
67863 0 1 2 11 10 3 9 4 8 5 6 7 12
98827 0 1 3 9 4 5 8 6 7 10 2 11 12
98828 0 1 3 9 4 5 8 6 7 11 2 10 12
98935 0 1 3 9 4 6 7 5 8 10 2 11 12
98936 0 1 3 9 4 6 7 5 8 11 2 10 12
99499 0 1 3 9 4 8 5 6 7 10 2 11 12
99500 0 1 3 9 4 8 5 6 7 11 2 10 12
112327 0 1 3 10 2 11 7 6 4 9 5 8 12
112329 0 1 3 10 2 11 7 6 5 8 4 9 12
112335 0 1 3 10 2 11 7 6 8 5 4 9 12
112375 0 1 3 10 2 11 8 5 7 6 4 9 12
112379 0 1 3 10 2 11 8 5 9 4 6 7 12
112407 0 1 3 10 2 11 9 4 5 8 6 7 12
112409 0 1 3 10 2 11 9 4 6 7 5 8 12
112419 0 1 3 10 2 11 9 4 8 5 6 7 12
112589 0 1 3 10 4 2 11 7 6 8 5 9 12
112603 0 1 3 10 4 2 11 9 5 8 6 7 12
112698 0 1 3 10 4 5 9 7 6 8 11 2 12
112706 0 1 3 10 4 5 9 8 6 7 11 2 12
112770 0 1 3 10 4 6 7 8 5 9 11 2 12
112778 0 1 3 10 4 6 7 9 5 8 11 2 12
113681 0 1 3 10 4 9 5 2 11 7 6 8 12
113682 0 1 3 10 4 9 5 2 11 8 6 7 12
113710 0 1 3 10 4 9 5 8 6 7 11 2 12
113715 0 1 3 10 4 9 5 8 7 6 2 11 12
113717 0 1 3 10 4 9 5 8 11 2 6 7 12
113842 0 1 3 10 4 9 7 6 5 8 11 2 12
113847 0 1 3 10 4 9 7 6 8 5 2 11 12
113882 0 1 3 10 4 9 8 5 6 7 11 2 12
113887 0 1 3 10 4 9 8 5 7 6 2 11 12
113919 0 1 3 10 4 9 11 2 5 8 6 7 12
113921 0 1 3 10 4 9 11 2 6 7 5 8 12
119311 0 1 3 10 7 6 2 11 8 5 4 9 12
119313 0 1 3 10 7 6 2 11 9 4 5 8 12
119338 0 1 3 10 7 6 4 9 5 8 11 2 12
119343 0 1 3 10 7 6 4 9 8 5 2 11 12
119345 0 1 3 10 7 6 4 9 11 2 5 8 12
119370 0 1 3 10 7 6 5 8 4 9 11 2 12
119375 0 1 3 10 7 6 5 8 9 4 2 11 12
119377 0 1 3 10 7 6 5 8 11 2 4 9 12
119458 0 1 3 10 7 6 8 5 4 9 11 2 12
119463 0 1 3 10 7 6 8 5 9 4 2 11 12
120499 0 1 3 10 8 5 2 11 7 6 4 9 12
120501 0 1 3 10 8 5 2 11 9 4 6 7 12
120531 0 1 3 10 8 5 4 9 7 6 2 11 12
120533 0 1 3 10 8 5 4 9 11 2 6 7 12
120563 0 1 3 10 8 5 6 7 9 4 2 11 12
120565 0 1 3 10 8 5 6 7 11 2 4 9 12
120646 0 1 3 10 8 5 7 6 4 9 11 2 12
120710 0 1 3 10 8 5 9 4 6 7 11 2 12
121687 0 1 3 10 9 4 2 11 7 6 5 8 12
121689 0 1 3 10 9 4 2 11 8 5 6 7 12
121714 0 1 3 10 9 4 5 8 6 7 11 2 12
121719 0 1 3 10 9 4 5 8 7 6 2 11 12
121721 0 1 3 10 9 4 5 8 11 2 6 7 12
121746 0 1 3 10 9 4 6 7 5 8 11 2 12
121751 0 1 3 10 9 4 6 7 8 5 2 11 12
121753 0 1 3 10 9 4 6 7 11 2 5 8 12
121898 0 1 3 10 9 4 8 5 6 7 11 2 12
121903 0 1 3 10 9 4 8 5 7 6 2 11 12
122867 0 1 3 10 11 2 4 9 5 8 6 7 12
122875 0 1 3 10 11 2 4 9 7 6 5 8 12
122877 0 1 3 10 11 2 4 9 8 5 6 7 12
122907 0 1 3 10 11 2 5 8 7 6 4 9 12
122909 0 1 3 10 11 2 5 8 9 4 6 7 12
122933 0 1 3 10 11 2 6 7 5 8 4 9 12
122939 0 1 3 10 11 2 6 7 8 5 4 9 12
122941 0 1 3 10 11 2 6 7 9 4 5 8 12
124529 0 1 3 11 2 4 10 5 9 7 6 8 12
124530 0 1 3 11 2 4 10 5 9 8 6 7 12
124541 0 1 3 11 2 4 10 7 6 8 5 9 12
124555 0 1 3 11 2 4 10 9 5 8 6 7 12
124603 0 1 3 11 2 5 8 6 7 9 4 10 12
124604 0 1 3 11 2 5 8 6 7 10 4 9 12
124637 0 1 3 11 2 5 9 4 10 7 6 8 12
124638 0 1 3 11 2 5 9 4 10 8 6 7 12
124711 0 1 3 11 2 6 7 5 8 9 4 10 12
124712 0 1 3 11 2 6 7 5 8 10 4 9 12
124721 0 1 3 11 2 6 7 8 5 9 4 10 12
124735 0 1 3 11 2 6 7 10 4 9 5 8 12
128034 0 1 3 11 4 10 7 6 8 9 5 2 12
128080 0 1 3 11 4 10 8 5 9 7 6 2 12
128094 0 1 3 11 4 10 8 6 7 9 5 2 12
128140 0 1 3 11 4 10 9 5 8 7 6 2 12
133290 0 1 3 11 7 6 8 5 9 10 4 2 12
133308 0 1 3 11 7 6 8 9 5 10 4 2 12
133316 0 1 3 11 7 6 8 10 4 9 5 2 12
134548 0 1 3 11 8 5 9 4 10 7 6 2 12
134892 0 1 3 11 8 6 7 9 5 10 4 2 12
134900 0 1 3 11 8 6 7 10 4 9 5 2 12
135852 0 1 3 11 9 4 10 7 6 8 5 2 12
135860 0 1 3 11 9 4 10 8 5 7 6 2 12
136146 0 1 3 11 9 5 8 6 7 10 4 2 12
137404 0 1 3 11 10 4 9 5 8 7 6 2 12
137436 0 1 3 11 10 4 9 7 6 8 5 2 12
137444 0 1 3 11 10 4 9 8 5 7 6 2 12
156113 0 1 4 8 5 6 7 9 3 10 2 11 12
156114 0 1 4 8 5 6 7 9 3 10 11 2 12
156122 0 1 4 8 5 6 7 10 3 9 11 2 12
156127 0 1 4 8 5 6 7 11 2 10 3 9 12
156365 0 1 4 8 5 7 6 2 11 9 3 10 12
156366 0 1 4 8 5 7 6 2 11 10 3 9 12
156367 0 1 4 8 5 7 6 3 9 10 2 11 12
156368 0 1 4 8 5 7 6 3 9 11 2 10 12
167947 0 1 4 9 3 5 8 6 7 10 2 11 12
167948 0 1 4 9 3 5 8 6 7 11 2 10 12
168055 0 1 4 9 3 6 7 5 8 10 2 11 12
168056 0 1 4 9 3 6 7 5 8 11 2 10 12
168967 0 1 4 9 3 10 2 11 7 6 5 8 12
168969 0 1 4 9 3 10 2 11 8 5 6 7 12
169138 0 1 4 9 3 10 7 6 5 8 11 2 12
169143 0 1 4 9 3 10 7 6 8 5 2 11 12
169178 0 1 4 9 3 10 8 5 6 7 11 2 12
169183 0 1 4 9 3 10 8 5 7 6 2 11 12
169215 0 1 4 9 3 10 11 2 5 8 6 7 12
169217 0 1 4 9 3 10 11 2 6 7 5 8 12
169745 0 1 4 9 5 2 11 3 10 7 6 8 12
169746 0 1 4 9 5 2 11 3 10 8 6 7 12
169853 0 1 4 9 5 3 10 2 11 7 6 8 12
169854 0 1 4 9 5 3 10 2 11 8 6 7 12
169866 0 1 4 9 5 3 10 7 6 8 11 2 12
169874 0 1 4 9 5 3 10 8 6 7 11 2 12
170567 0 1 4 9 5 8 6 7 10 3 2 11 12
170568 0 1 4 9 5 8 6 7 10 3 11 2 12
170569 0 1 4 9 5 8 6 7 11 2 3 10 12
170647 0 1 4 9 5 8 7 6 2 11 3 10 12
170649 0 1 4 9 5 8 7 6 3 10 2 11 12
170650 0 1 4 9 5 8 7 6 3 10 11 2 12
170690 0 1 4 9 5 8 10 3 6 7 11 2 12
170699 0 1 4 9 5 8 10 3 11 2 6 7 12
170704 0 1 4 9 5 8 10 3 11 7 6 2 12
170739 0 1 4 9 5 8 11 2 10 3 6 7 12
170764 0 1 4 9 5 8 11 3 10 7 6 2 12
174607 0 1 4 9 7 6 2 11 8 5 3 10 12
174609 0 1 4 9 7 6 2 11 10 3 5 8 12
174639 0 1 4 9 7 6 3 10 8 5 2 11 12
174641 0 1 4 9 7 6 3 10 11 2 5 8 12
174671 0 1 4 9 7 6 5 8 10 3 2 11 12
174672 0 1 4 9 7 6 5 8 10 3 11 2 12
174673 0 1 4 9 7 6 5 8 11 2 3 10 12
174751 0 1 4 9 7 6 8 5 2 11 3 10 12
174753 0 1 4 9 7 6 8 5 3 10 2 11 12
174754 0 1 4 9 7 6 8 5 3 10 11 2 12
175795 0 1 4 9 8 5 2 11 7 6 3 10 12
175797 0 1 4 9 8 5 2 11 10 3 6 7 12
175827 0 1 4 9 8 5 3 10 7 6 2 11 12
175829 0 1 4 9 8 5 3 10 11 2 6 7 12
175859 0 1 4 9 8 5 6 7 10 3 2 11 12
175860 0 1 4 9 8 5 6 7 10 3 11 2 12
175861 0 1 4 9 8 5 6 7 11 2 3 10 12
175939 0 1 4 9 8 5 7 6 2 11 3 10 12
175941 0 1 4 9 8 5 7 6 3 10 2 11 12
175942 0 1 4 9 8 5 7 6 3 10 11 2 12
176983 0 1 4 9 10 3 2 11 7 6 5 8 12
176985 0 1 4 9 10 3 2 11 8 5 6 7 12
177010 0 1 4 9 10 3 5 8 6 7 11 2 12
177015 0 1 4 9 10 3 5 8 7 6 2 11 12
177017 0 1 4 9 10 3 5 8 11 2 6 7 12
177042 0 1 4 9 10 3 6 7 5 8 11 2 12
177047 0 1 4 9 10 3 6 7 8 5 2 11 12
177049 0 1 4 9 10 3 6 7 11 2 5 8 12
177255 0 1 4 9 10 3 11 2 5 8 6 7 12
177257 0 1 4 9 10 3 11 2 6 7 5 8 12
177324 0 1 4 9 10 3 11 7 6 8 5 2 12
177332 0 1 4 9 10 3 11 8 5 7 6 2 12
178171 0 1 4 9 11 2 3 10 7 6 5 8 12
178173 0 1 4 9 11 2 3 10 8 5 6 7 12
178203 0 1 4 9 11 2 5 8 7 6 3 10 12
178205 0 1 4 9 11 2 5 8 10 3 6 7 12
178235 0 1 4 9 11 2 6 7 8 5 3 10 12
178237 0 1 4 9 11 2 6 7 10 3 5 8 12
178443 0 1 4 9 11 2 10 3 5 8 6 7 12
178445 0 1 4 9 11 2 10 3 6 7 5 8 12
178908 0 1 4 9 11 3 10 7 6 8 5 2 12
178916 0 1 4 9 11 3 10 8 5 7 6 2 12
181709 0 1 4 10 3 2 11 7 6 8 5 9 12
181723 0 1 4 10 3 2 11 9 5 8 6 7 12
181818 0 1 4 10 3 5 9 7 6 8 11 2 12
181826 0 1 4 10 3 5 9 8 6 7 11 2 12
181890 0 1 4 10 3 6 7 8 5 9 11 2 12
181898 0 1 4 10 3 6 7 9 5 8 11 2 12
183101 0 1 4 10 3 11 2 5 9 7 6 8 12
183102 0 1 4 10 3 11 2 5 9 8 6 7 12
183103 0 1 4 10 3 11 2 6 7 8 5 9 12
183104 0 1 4 10 3 11 2 6 7 9 5 8 12
183330 0 1 4 10 3 11 7 6 8 9 5 2 12
183376 0 1 4 10 3 11 8 5 9 7 6 2 12
183390 0 1 4 10 3 11 8 6 7 9 5 2 12
183436 0 1 4 10 3 11 9 5 8 7 6 2 12
184842 0 1 4 10 5 9 7 6 8 11 3 2 12
184902 0 1 4 10 5 9 8 6 7 11 3 2 12
188586 0 1 4 10 7 6 8 5 9 11 3 2 12
188602 0 1 4 10 7 6 8 9 5 3 11 2 12
189874 0 1 4 10 8 5 9 7 6 3 11 2 12
190186 0 1 4 10 8 6 7 9 5 3 11 2 12
191442 0 1 4 10 9 5 8 6 7 11 3 2 12
191458 0 1 4 10 9 5 8 7 6 3 11 2 12
213089 0 1 5 7 6 2 11 3 10 8 4 9 12
213090 0 1 5 7 6 2 11 3 10 9 4 8 12
213101 0 1 5 7 6 2 11 8 4 9 3 10 12
213115 0 1 5 7 6 2 11 10 3 9 4 8 12
213163 0 1 5 7 6 3 9 4 8 10 2 11 12
213164 0 1 5 7 6 3 9 4 8 11 2 10 12
213197 0 1 5 7 6 3 10 2 11 8 4 9 12
213198 0 1 5 7 6 3 10 2 11 9 4 8 12
213210 0 1 5 7 6 3 10 8 4 9 11 2 12
213218 0 1 5 7 6 3 10 9 4 8 11 2 12
213271 0 1 5 7 6 4 8 3 9 10 2 11 12
213272 0 1 5 7 6 4 8 3 9 11 2 10 12
213281 0 1 5 7 6 4 8 9 3 10 2 11 12
213282 0 1 5 7 6 4 8 9 3 10 11 2 12
213290 0 1 5 7 6 4 8 10 3 9 11 2 12
213295 0 1 5 7 6 4 8 11 2 10 3 9 12
225233 0 1 5 8 4 6 7 9 3 10 2 11 12
225234 0 1 5 8 4 6 7 9 3 10 11 2 12
225242 0 1 5 8 4 6 7 10 3 9 11 2 12
225247 0 1 5 8 4 6 7 11 2 10 3 9 12
225787 0 1 5 8 4 9 3 6 7 10 2 11 12
225788 0 1 5 8 4 9 3 6 7 11 2 10 12
225819 0 1 5 8 4 9 3 10 7 6 2 11 12
225821 0 1 5 8 4 9 3 10 11 2 6 7 12
225943 0 1 5 8 4 9 7 6 2 11 3 10 12
225945 0 1 5 8 4 9 7 6 3 10 2 11 12
225946 0 1 5 8 4 9 7 6 3 10 11 2 12
225986 0 1 5 8 4 9 10 3 6 7 11 2 12
225995 0 1 5 8 4 9 10 3 11 2 6 7 12
226000 0 1 5 8 4 9 10 3 11 7 6 2 12
226035 0 1 5 8 4 9 11 2 10 3 6 7 12
226060 0 1 5 8 4 9 11 3 10 7 6 2 12
227455 0 1 5 8 6 7 9 4 2 11 3 10 12
227457 0 1 5 8 6 7 9 4 3 10 2 11 12
227458 0 1 5 8 6 7 9 4 3 10 11 2 12
227463 0 1 5 8 6 7 9 4 10 3 2 11 12
227464 0 1 5 8 6 7 9 4 10 3 11 2 12
227466 0 1 5 8 6 7 9 4 10 11 3 2 12
227498 0 1 5 8 6 7 10 3 4 9 11 2 12
227503 0 1 5 8 6 7 10 3 9 4 2 11 12
227507 0 1 5 8 6 7 10 3 11 2 4 9 12
227512 0 1 5 8 6 7 10 3 11 9 4 2 12
227526 0 1 5 8 6 7 10 4 9 11 3 2 12
227535 0 1 5 8 6 7 11 2 3 10 4 9 12
227537 0 1 5 8 6 7 11 2 4 9 3 10 12
227547 0 1 5 8 6 7 11 2 10 3 4 9 12
227572 0 1 5 8 6 7 11 3 10 9 4 2 12
229895 0 1 5 8 7 6 2 11 3 10 4 9 12
229903 0 1 5 8 7 6 2 11 9 4 3 10 12
229905 0 1 5 8 7 6 2 11 10 3 4 9 12
229930 0 1 5 8 7 6 3 10 4 9 11 2 12
229935 0 1 5 8 7 6 3 10 9 4 2 11 12
229937 0 1 5 8 7 6 3 10 11 2 4 9 12
229961 0 1 5 8 7 6 4 9 3 10 2 11 12
229962 0 1 5 8 7 6 4 9 3 10 11 2 12
229967 0 1 5 8 7 6 4 9 10 3 2 11 12
229968 0 1 5 8 7 6 4 9 10 3 11 2 12
229969 0 1 5 8 7 6 4 9 11 2 3 10 12
231091 0 1 5 8 9 4 2 11 7 6 3 10 12
231093 0 1 5 8 9 4 2 11 10 3 6 7 12
231123 0 1 5 8 9 4 3 10 7 6 2 11 12
231125 0 1 5 8 9 4 3 10 11 2 6 7 12
231155 0 1 5 8 9 4 6 7 10 3 2 11 12
231156 0 1 5 8 9 4 6 7 10 3 11 2 12
231157 0 1 5 8 9 4 6 7 11 2 3 10 12
231302 0 1 5 8 9 4 10 3 6 7 11 2 12
231311 0 1 5 8 9 4 10 3 11 2 6 7 12
231316 0 1 5 8 9 4 10 3 11 7 6 2 12
231346 0 1 5 8 9 4 10 7 6 3 11 2 12
232279 0 1 5 8 10 3 2 11 7 6 4 9 12
232281 0 1 5 8 10 3 2 11 9 4 6 7 12
232311 0 1 5 8 10 3 4 9 7 6 2 11 12
232313 0 1 5 8 10 3 4 9 11 2 6 7 12
232343 0 1 5 8 10 3 6 7 9 4 2 11 12
232345 0 1 5 8 10 3 6 7 11 2 4 9 12
232490 0 1 5 8 10 3 9 4 6 7 11 2 12
232930 0 1 5 8 10 4 9 7 6 3 11 2 12
233467 0 1 5 8 11 2 3 10 7 6 4 9 12
233469 0 1 5 8 11 2 3 10 9 4 6 7 12
233499 0 1 5 8 11 2 4 9 7 6 3 10 12
233501 0 1 5 8 11 2 4 9 10 3 6 7 12
233531 0 1 5 8 11 2 6 7 9 4 3 10 12
233533 0 1 5 8 11 2 6 7 10 3 4 9 12
233751 0 1 5 8 11 2 10 3 9 4 6 7 12
234172 0 1 5 8 11 3 10 4 9 7 6 2 12
238865 0 1 5 9 4 2 11 3 10 7 6 8 12
238866 0 1 5 9 4 2 11 3 10 8 6 7 12
238973 0 1 5 9 4 3 10 2 11 7 6 8 12
238974 0 1 5 9 4 3 10 2 11 8 6 7 12
238986 0 1 5 9 4 3 10 7 6 8 11 2 12
238994 0 1 5 9 4 3 10 8 6 7 11 2 12
239969 0 1 5 9 4 10 3 2 11 7 6 8 12
239970 0 1 5 9 4 10 3 2 11 8 6 7 12
240138 0 1 5 9 4 10 7 6 8 11 3 2 12
240198 0 1 5 9 4 10 8 6 7 11 3 2 12
243898 0 1 5 9 7 6 8 10 4 3 11 2 12
243900 0 1 5 9 7 6 8 10 4 11 3 2 12
243908 0 1 5 9 7 6 8 11 3 10 4 2 12
245482 0 1 5 9 8 6 7 10 4 3 11 2 12
245484 0 1 5 9 8 6 7 10 4 11 3 2 12
245492 0 1 5 9 8 6 7 11 3 10 4 2 12
282209 0 1 6 7 5 2 11 3 10 8 4 9 12
282210 0 1 6 7 5 2 11 3 10 9 4 8 12
282221 0 1 6 7 5 2 11 8 4 9 3 10 12
282235 0 1 6 7 5 2 11 10 3 9 4 8 12
282283 0 1 6 7 5 3 9 4 8 10 2 11 12
282284 0 1 6 7 5 3 9 4 8 11 2 10 12
282317 0 1 6 7 5 3 10 2 11 8 4 9 12
282318 0 1 6 7 5 3 10 2 11 9 4 8 12
282330 0 1 6 7 5 3 10 8 4 9 11 2 12
282338 0 1 6 7 5 3 10 9 4 8 11 2 12
282391 0 1 6 7 5 4 8 3 9 10 2 11 12
282392 0 1 6 7 5 4 8 3 9 11 2 10 12
282401 0 1 6 7 5 4 8 9 3 10 2 11 12
282402 0 1 6 7 5 4 8 9 3 10 11 2 12
282410 0 1 6 7 5 4 8 10 3 9 11 2 12
282415 0 1 6 7 5 4 8 11 2 10 3 9 12
282653 0 1 6 7 5 8 4 2 11 9 3 10 12
282654 0 1 6 7 5 8 4 2 11 10 3 9 12
282655 0 1 6 7 5 8 4 3 9 10 2 11 12
282656 0 1 6 7 5 8 4 3 9 11 2 10 12
282665 0 1 6 7 5 8 4 9 3 10 2 11 12
282666 0 1 6 7 5 8 4 9 3 10 11 2 12
282671 0 1 6 7 5 8 4 9 10 3 2 11 12
282672 0 1 6 7 5 8 4 9 10 3 11 2 12
282673 0 1 6 7 5 8 4 9 11 2 3 10 12
282751 0 1 6 7 5 8 9 4 2 11 3 10 12
282753 0 1 6 7 5 8 9 4 3 10 2 11 12
282754 0 1 6 7 5 8 9 4 3 10 11 2 12
282759 0 1 6 7 5 8 9 4 10 3 2 11 12
282760 0 1 6 7 5 8 9 4 10 3 11 2 12
282762 0 1 6 7 5 8 9 4 10 11 3 2 12
282794 0 1 6 7 5 8 10 3 4 9 11 2 12
282799 0 1 6 7 5 8 10 3 9 4 2 11 12
282803 0 1 6 7 5 8 10 3 11 2 4 9 12
282808 0 1 6 7 5 8 10 3 11 9 4 2 12
282822 0 1 6 7 5 8 10 4 9 11 3 2 12
282831 0 1 6 7 5 8 11 2 3 10 4 9 12
282833 0 1 6 7 5 8 11 2 4 9 3 10 12
282843 0 1 6 7 5 8 11 2 10 3 4 9 12
282868 0 1 6 7 5 8 11 3 10 9 4 2 12
285191 0 1 6 7 8 5 2 11 3 10 4 9 12
285199 0 1 6 7 8 5 2 11 9 4 3 10 12
285201 0 1 6 7 8 5 2 11 10 3 4 9 12
285226 0 1 6 7 8 5 3 10 4 9 11 2 12
285231 0 1 6 7 8 5 3 10 9 4 2 11 12
285233 0 1 6 7 8 5 3 10 11 2 4 9 12
285257 0 1 6 7 8 5 4 9 3 10 2 11 12
285258 0 1 6 7 8 5 4 9 3 10 11 2 12
285263 0 1 6 7 8 5 4 9 10 3 2 11 12
285264 0 1 6 7 8 5 4 9 10 3 11 2 12
285265 0 1 6 7 8 5 4 9 11 2 3 10 12
285343 0 1 6 7 8 5 9 4 2 11 3 10 12
285345 0 1 6 7 8 5 9 4 3 10 2 11 12
285346 0 1 6 7 8 5 9 4 3 10 11 2 12
285351 0 1 6 7 8 5 9 4 10 3 2 11 12
285352 0 1 6 7 8 5 9 4 10 3 11 2 12
285354 0 1 6 7 8 5 9 4 10 11 3 2 12
285370 0 1 6 7 8 5 9 10 4 3 11 2 12
285372 0 1 6 7 8 5 9 10 4 11 3 2 12
285380 0 1 6 7 8 5 9 11 3 10 4 2 12
286387 0 1 6 7 9 4 2 11 8 5 3 10 12
286389 0 1 6 7 9 4 2 11 10 3 5 8 12
286419 0 1 6 7 9 4 3 10 8 5 2 11 12
286421 0 1 6 7 9 4 3 10 11 2 5 8 12
286451 0 1 6 7 9 4 5 8 10 3 2 11 12
286452 0 1 6 7 9 4 5 8 10 3 11 2 12
286453 0 1 6 7 9 4 5 8 11 2 3 10 12
286531 0 1 6 7 9 4 8 5 2 11 3 10 12
286533 0 1 6 7 9 4 8 5 3 10 2 11 12
286534 0 1 6 7 9 4 8 5 3 10 11 2 12
286598 0 1 6 7 9 4 10 3 5 8 11 2 12
286607 0 1 6 7 9 4 10 3 11 2 5 8 12
286612 0 1 6 7 9 4 10 3 11 8 5 2 12
286642 0 1 6 7 9 4 10 8 5 3 11 2 12
286954 0 1 6 7 9 5 8 10 4 3 11 2 12
286956 0 1 6 7 9 5 8 10 4 11 3 2 12
286964 0 1 6 7 9 5 8 11 3 10 4 2 12
287575 0 1 6 7 10 3 2 11 8 5 4 9 12
287577 0 1 6 7 10 3 2 11 9 4 5 8 12
287602 0 1 6 7 10 3 4 9 5 8 11 2 12
287607 0 1 6 7 10 3 4 9 8 5 2 11 12
287609 0 1 6 7 10 3 4 9 11 2 5 8 12
287634 0 1 6 7 10 3 5 8 4 9 11 2 12
287639 0 1 6 7 10 3 5 8 9 4 2 11 12
287641 0 1 6 7 10 3 5 8 11 2 4 9 12
287786 0 1 6 7 10 3 9 4 5 8 11 2 12
287791 0 1 6 7 10 3 9 4 8 5 2 11 12
287847 0 1 6 7 10 3 11 2 4 9 5 8 12
287849 0 1 6 7 10 3 11 2 5 8 4 9 12
287916 0 1 6 7 10 3 11 8 5 9 4 2 12
287924 0 1 6 7 10 3 11 9 4 8 5 2 12
288210 0 1 6 7 10 4 9 5 8 11 3 2 12
288226 0 1 6 7 10 4 9 8 5 3 11 2 12
288755 0 1 6 7 11 2 3 10 4 9 5 8 12
288763 0 1 6 7 11 2 3 10 8 5 4 9 12
288765 0 1 6 7 11 2 3 10 9 4 5 8 12
288795 0 1 6 7 11 2 4 9 8 5 3 10 12
288797 0 1 6 7 11 2 4 9 10 3 5 8 12
288821 0 1 6 7 11 2 5 8 4 9 3 10 12
288827 0 1 6 7 11 2 5 8 9 4 3 10 12
288829 0 1 6 7 11 2 5 8 10 3 4 9 12
289035 0 1 6 7 11 2 10 3 4 9 5 8 12
289037 0 1 6 7 11 2 10 3 5 8 4 9 12
289047 0 1 6 7 11 2 10 3 9 4 5 8 12
289468 0 1 6 7 11 3 10 4 9 8 5 2 12
289500 0 1 6 7 11 3 10 8 5 9 4 2 12
289508 0 1 6 7 11 3 10 9 4 8 5 2 12
795965 0 1 11 2 3 10 4 5 9 7 6 8 12
795966 0 1 11 2 3 10 4 5 9 8 6 7 12
795967 0 1 11 2 3 10 4 6 7 8 5 9 12
795968 0 1 11 2 3 10 4 6 7 9 5 8 12
796007 0 1 11 2 3 10 4 9 5 8 6 7 12
796015 0 1 11 2 3 10 4 9 7 6 5 8 12
796017 0 1 11 2 3 10 4 9 8 5 6 7 12
796183 0 1 11 2 3 10 7 6 4 9 5 8 12
796185 0 1 11 2 3 10 7 6 5 8 4 9 12
796191 0 1 11 2 3 10 7 6 8 5 4 9 12
796231 0 1 11 2 3 10 8 5 7 6 4 9 12
796235 0 1 11 2 3 10 8 5 9 4 6 7 12
796263 0 1 11 2 3 10 9 4 5 8 6 7 12
796265 0 1 11 2 3 10 9 4 6 7 5 8 12
796275 0 1 11 2 3 10 9 4 8 5 6 7 12
796747 0 1 11 2 4 8 5 6 7 9 3 10 12
796748 0 1 11 2 4 8 5 6 7 10 3 9 12
797095 0 1 11 2 4 9 3 10 7 6 5 8 12
797097 0 1 11 2 4 9 3 10 8 5 6 7 12
797105 0 1 11 2 4 9 5 3 10 7 6 8 12
797106 0 1 11 2 4 9 5 3 10 8 6 7 12
797139 0 1 11 2 4 9 5 8 7 6 3 10 12
797141 0 1 11 2 4 9 5 8 10 3 6 7 12
797271 0 1 11 2 4 9 7 6 8 5 3 10 12
797311 0 1 11 2 4 9 8 5 7 6 3 10 12
797343 0 1 11 2 4 9 10 3 5 8 6 7 12
797345 0 1 11 2 4 9 10 3 6 7 5 8 12
797405 0 1 11 2 4 10 3 5 9 7 6 8 12
797406 0 1 11 2 4 10 3 5 9 8 6 7 12
797407 0 1 11 2 4 10 3 6 7 8 5 9 12
797408 0 1 11 2 4 10 3 6 7 9 5 8 12
797885 0 1 11 2 5 7 6 3 10 8 4 9 12
797886 0 1 11 2 5 7 6 3 10 9 4 8 12
797887 0 1 11 2 5 7 6 4 8 9 3 10 12
797888 0 1 11 2 5 7 6 4 8 10 3 9 12
798187 0 1 11 2 5 8 4 6 7 9 3 10 12
798188 0 1 11 2 5 8 4 6 7 10 3 9 12
798219 0 1 11 2 5 8 4 9 7 6 3 10 12
798221 0 1 11 2 5 8 4 9 10 3 6 7 12
798263 0 1 11 2 5 8 6 7 9 4 3 10 12
798265 0 1 11 2 5 8 6 7 10 3 4 9 12
798343 0 1 11 2 5 8 7 6 3 10 4 9 12
798345 0 1 11 2 5 8 7 6 4 9 3 10 12
798395 0 1 11 2 5 8 9 4 10 3 6 7 12
798435 0 1 11 2 5 8 10 3 9 4 6 7 12
798545 0 1 11 2 5 9 4 3 10 7 6 8 12
798546 0 1 11 2 5 9 4 3 10 8 6 7 12
799325 0 1 11 2 6 7 5 3 10 8 4 9 12
799326 0 1 11 2 6 7 5 3 10 9 4 8 12
799327 0 1 11 2 6 7 5 4 8 9 3 10 12
799328 0 1 11 2 6 7 5 4 8 10 3 9 12
799337 0 1 11 2 6 7 5 8 4 9 3 10 12
799343 0 1 11 2 6 7 5 8 9 4 3 10 12
799345 0 1 11 2 6 7 5 8 10 3 4 9 12
799423 0 1 11 2 6 7 8 5 3 10 4 9 12
799425 0 1 11 2 6 7 8 5 4 9 3 10 12
799431 0 1 11 2 6 7 8 5 9 4 3 10 12
799471 0 1 11 2 6 7 9 4 8 5 3 10 12
799475 0 1 11 2 6 7 9 4 10 3 5 8 12
799503 0 1 11 2 6 7 10 3 4 9 5 8 12
799505 0 1 11 2 6 7 10 3 5 8 4 9 12
799515 0 1 11 2 6 7 10 3 9 4 5 8 12
807587 0 1 11 2 10 3 4 9 5 8 6 7 12
807595 0 1 11 2 10 3 4 9 7 6 5 8 12
807597 0 1 11 2 10 3 4 9 8 5 6 7 12
807627 0 1 11 2 10 3 5 8 7 6 4 9 12
807629 0 1 11 2 10 3 5 8 9 4 6 7 12
807653 0 1 11 2 10 3 6 7 5 8 4 9 12
807659 0 1 11 2 10 3 6 7 8 5 4 9 12
807661 0 1 11 2 10 3 6 7 9 4 5 8 12
807867 0 1 11 2 10 3 9 4 5 8 6 7 12
807869 0 1 11 2 10 3 9 4 6 7 5 8 12
807879 0 1 11 2 10 3 9 4 8 5 6 7 12
809323 0 1 11 2 10 7 6 3 9 4 5 8 12
809331 0 1 11 2 10 7 6 4 8 5 3 9 12
809335 0 1 11 2 10 7 6 4 9 3 5 8 12
809343 0 1 11 2 10 7 6 5 8 4 3 9 12
809451 0 1 11 2 10 8 4 5 7 6 3 9 12
809463 0 1 11 2 10 8 4 6 7 5 3 9 12
809503 0 1 11 2 10 8 5 3 9 4 6 7 12
809515 0 1 11 2 10 8 5 4 9 3 6 7 12
809623 0 1 11 2 10 9 3 4 8 5 6 7 12
809631 0 1 11 2 10 9 3 5 7 6 4 8 12
809635 0 1 11 2 10 9 3 5 8 4 6 7 12
809643 0 1 11 2 10 9 3 6 7 5 4 8 12
877419 0 1 11 7 6 2 10 3 4 9 5 8 12
877421 0 1 11 7 6 2 10 3 5 8 4 9 12
877431 0 1 11 7 6 2 10 3 9 4 5 8 12
877615 0 1 11 7 6 3 9 4 8 5 2 10 12
877671 0 1 11 7 6 3 10 2 4 9 5 8 12
877673 0 1 11 7 6 3 10 2 5 8 4 9 12
877795 0 1 11 7 6 4 8 5 2 10 3 9 12
877797 0 1 11 7 6 4 8 5 3 9 2 10 12
877871 0 1 11 7 6 4 9 3 10 2 5 8 12
878047 0 1 11 7 6 5 8 4 2 10 3 9 12
878049 0 1 11 7 6 5 8 4 3 9 2 10 12
878055 0 1 11 7 6 5 8 4 9 3 2 10 12
878443 0 1 11 7 6 8 5 2 10 3 4 9 12
878451 0 1 11 7 6 8 5 3 9 4 2 10 12
878455 0 1 11 7 6 8 5 3 10 2 4 9 12
878463 0 1 11 7 6 8 5 4 9 3 2 10 12
883411 0 1 11 8 4 5 7 6 2 10 3 9 12
883413 0 1 11 8 4 5 7 6 3 9 2 10 12
883663 0 1 11 8 4 6 7 5 2 10 3 9 12
883665 0 1 11 8 4 6 7 5 3 9 2 10 12
884235 0 1 11 8 4 9 3 5 7 6 2 10 12
884247 0 1 11 8 4 9 3 6 7 5 2 10 12
884919 0 1 11 8 5 2 10 3 9 4 6 7 12
885359 0 1 11 8 5 4 9 3 10 2 6 7 12
885931 0 1 11 8 5 7 6 2 10 3 4 9 12
885939 0 1 11 8 5 7 6 3 9 4 2 10 12
885943 0 1 11 8 5 7 6 3 10 2 4 9 12
885951 0 1 11 8 5 7 6 4 9 3 2 10 12
886159 0 1 11 8 5 9 4 2 10 3 6 7 12
886171 0 1 11 8 5 9 4 3 10 2 6 7 12
890719 0 1 11 9 3 4 8 5 7 6 2 10 12
891159 0 1 11 9 3 6 7 5 8 4 2 10 12
891723 0 1 11 9 3 8 4 5 7 6 2 10 12
891735 0 1 11 9 3 8 4 6 7 5 2 10 12
891943 0 1 11 9 3 10 2 4 8 5 6 7 12
891951 0 1 11 9 3 10 2 5 7 6 4 8 12
891955 0 1 11 9 3 10 2 5 8 4 6 7 12
891963 0 1 11 9 3 10 2 6 7 5 4 8 12
892395 0 1 11 9 4 2 10 3 5 8 6 7 12
892397 0 1 11 9 4 2 10 3 6 7 5 8 12
892647 0 1 11 9 4 3 10 2 5 8 6 7 12
892649 0 1 11 9 4 3 10 2 6 7 5 8 12
893647 0 1 11 9 4 8 5 2 10 3 6 7 12
893659 0 1 11 9 4 8 5 3 10 2 6 7 12
898011 0 1 11 10 2 3 9 4 5 8 6 7 12
898013 0 1 11 10 2 3 9 4 6 7 5 8 12
898023 0 1 11 10 2 3 9 4 8 5 6 7 12
898207 0 1 11 10 2 4 8 5 7 6 3 9 12
898263 0 1 11 10 2 4 9 3 5 8 6 7 12
898265 0 1 11 10 2 4 9 3 6 7 5 8 12
898387 0 1 11 10 2 5 7 6 3 9 4 8 12
898389 0 1 11 10 2 5 7 6 4 8 3 9 12
898463 0 1 11 10 2 5 8 4 9 3 6 7 12
898639 0 1 11 10 2 6 7 5 3 9 4 8 12
898641 0 1 11 10 2 6 7 5 4 8 3 9 12
898647 0 1 11 10 2 6 7 5 8 4 3 9 12
899431 0 1 11 10 2 9 3 4 8 5 6 7 12
899439 0 1 11 10 2 9 3 5 7 6 4 8 12
899443 0 1 11 10 2 9 3 5 8 4 6 7 12
899451 0 1 11 10 2 9 3 6 7 5 4 8 12
L= 907200
Crossings, #
0 616 =2*A079410(6)
1 2612
2 6578
3 13258
4 22951
5 34551
6 47558
7 60164
8 69805
9 76233
10 78956
11 75608
12 68885
13 61388
14 52725
15 45361
16 38418
17 31105
18 27315
19 23763
20 18121
21 14565
22 11554
23 8148
24 5697
25 3467
26 2443
27 1756
28 969
29 554
30 513
31 523
32 290
33 154
34 214
35 183
36 60
37 39
38 52
39 32
41 7
42 8
45 1 (45=A000384(5))
--------------------------------------------------------------------
N = 7
L= 79315200
Crossings, #
0 5780 =2*A079410(7)
1 28062
2 83830
3 192946
4 378774
5 652995
6 1025455
7 1488574
8 2024878
9 2597909
10 3185399
11 3742655
12 4231953
13 4637975
14 4941540
15 5104362
16 5148296
17 5042115
18 4789037
19 4453230
20 4025845
21 3536097
22 3056490
23 2599872
24 2182056
25 1829128
26 1504727
27 1284212
28 1069388
29 915349
30 752362
31 632230
32 525210
33 417623
34 323570
35 246352
36 189223
37 136818
38 93125
39 65577
40 48613
41 34123
42 21734
43 15337
44 13916
45 10476
46 6528
47 5303
48 5647
49 3804
50 2168
51 1898
52 1858
53 1048
54 467
55 492
56 408
57 142
58 62
59 86
60 51
62 9
63 10
66 1 (66=A000384(6))
-------------------------------------------------------------------
N = 8
L= 9551001600
Crossings, #
0 51528 =2*A079410(8)
1 299128
2 1045172
3 2780302
4 6241794
5 12310016
6 22018027
7 36369449
8 56245840
9 82114752
10 114073821
11 151498103
12 193255370
13 237674310
14 282768258
15 326264220
16 366219004
17 400886775
18 428991734
19 449812265
20 463375382
21 469945084
22 469948095
23 464068336
24 452851598
25 437142549
26 416958503
27 392759346
28 365523227
29 335717866
30 303915875
31 271198770
32 238486590
33 207406633
34 177902473
35 151055613
36 127087332
37 106812272
38 89629695
39 74832580
40 62740058
41 53131645
42 44893184
43 37717620
44 31840339
45 26722499
46 22410053
47 18268639
48 14828064
49 11948620
50 9504110
51 7287812
52 5537479
53 4238549
54 3194655
55 2324204
56 1662612
57 1259014
58 959752
59 683270
60 489526
61 400773
62 333114
63 240187
64 176184
65 159831
66 134829
67 92655
68 67071
69 62041
70 48732
71 29986
72 21164
73 19436
74 13486
75 7200
76 5028
77 4596
78 2596
79 1054
80 910
81 753
82 268
83 89
84 128
85 74
87 11
88 12
91 1 (91=A000384(7))