E623 Le tournoi de belote [**** à la main]
Alain Esculier a apporté des solutions pour les valeurs de n allant de 8 à 76.
Il signale tout d’abord que Robert Ferréol a mis en ligne un article très intéressant et très documenté sur ce problème
:http://mapage.noos.fr/r.ferreol/atelecharger/textes/tournoi%20de%20belote.doc.
Par ailleurs il précise que dans le numéro de décembre 1988 de la revue Pour La Science, Ian Stewart a posé le même problème à propos d'un concours de tambours et a donné la réponse suivante pour n = 12 sans donner d’explication :
1) AB - IL EJ - GK FH - CD 2) AC - JB FK - HL GI - DE 3) AD - KC GL - IB HJ - EF 4) AE - LD HB - JC IK - FG 5) AF - BE IC - KD JL - GH 6) AG - CF JD - LE KB - HI 7) AH - DG KE - BF LC - IJ 8) AI - EH LF - CG BD - JK 9) AJ - FI BG - DH CE - KL 10) AK - GJ CH - EI DF - LB 11) AL - HK DI - FJ EG – BC
Revenant au concours de belote lui-même, Alain Esculier donne des solutions pour de petites valeurs de n = 8, 12, 16,20.
( notation : deux partenaires [i,j] ; une tablée [[i,j],[k,l]] ; un tour [ tablée1,tablée2 ...]
===============================================
n=8
1 --> [[[1, 2], [5, 7]], [[6, 8], [3, 4]]]
2 --> [[[1, 3], [2, 4]], [[7, 8], [5, 6]]]
3 --> [[[1, 4], [6, 7]], [[5, 8], [2, 3]]]
4 --> [[[1, 5], [3, 6]], [[4, 8], [2, 7]]]
5 --> [[[1, 6], [2, 8]], [[3, 5], [4, 7]]]
6 --> [[[1, 7], [3, 8]], [[4, 6], [2, 5]]]
7 --> [[[1, 8], [4, 5]], [[2, 6], [3, 7]]]
1 --> [[[1, 2], [3, 7]], [[4, 5], [6, 8]]]
2 --> [[[1, 3], [4, 8]], [[5, 6], [7, 2]]]
3 --> [[[1, 4], [5, 2]], [[6, 7], [8, 3]]]
4 --> [[[1, 5], [6, 3]], [[7, 8], [2, 4]]]
5 --> [[[1, 6], [7, 4]], [[8, 2], [3, 5]]]
6 --> [[[1, 7], [8, 5]], [[2, 3], [4, 6]]]
7 --> [[[1, 8], [2, 6]], [[3, 4], [5, 7]]]
==========================================
n=12
1 --> [[[1, 2], [7, 9]], [[10, 3], [11, 8]], [[4, 5], [6, 12]]]
2 --> [[[1, 3], [8, 10]], [[11, 4], [12, 9]], [[5, 6], [7, 2]]]
3 --> [[[1, 4], [9, 11]], [[12, 5], [2, 10]], [[6, 7], [8, 3]]]
4 --> [[[1, 5], [10, 12]], [[2, 6], [3, 11]], [[7, 8], [9, 4]]]
5 --> [[[1, 6], [11, 2]], [[3, 7], [4, 12]], [[8, 9], [10, 5]]]
6 --> [[[1, 7], [12, 3]], [[4, 8], [5, 2]], [[9, 10], [11, 6]]]
7 --> [[[1, 8], [2, 4]], [[5, 9], [6, 3]], [[10, 11], [12, 7]]]
8 --> [[[1, 9], [3, 5]], [[6, 10], [7, 4]], [[11, 12], [2, 8]]]
9 --> [[[1, 10], [4, 6]], [[7, 11], [8, 5]], [[12, 2], [3, 9]]]
10 --> [[[1, 11], [5, 7]], [[8, 12], [9, 6]], [[2, 3], [4, 10]]]
11 --> [[[1, 12], [6, 8]], [[9, 2], [10, 7]], [[3, 4], [5, 11]]]
1 --> [[[1, 2], [8, 11]], [[12, 6], [4, 5]], [[9, 7], [3, 10]]]
2 --> [[[1, 3], [9, 12]], [[2, 7], [5, 6]], [[10, 8], [4, 11]]]
3 --> [[[1, 4], [10, 2]], [[3, 8], [6, 7]], [[11, 9], [5, 12]]]
4 --> [[[1, 5], [11, 3]], [[4, 9], [7, 8]], [[12, 10], [6, 2]]]
5 --> [[[1, 6], [12, 4]], [[5, 10], [8, 9]], [[2, 11], [7, 3]]]
6 --> [[[1, 7], [2, 5]], [[6, 11], [9, 10]], [[3, 12], [8, 4]]]
7 --> [[[1, 8], [3, 6]], [[7, 12], [10, 11]], [[4, 2], [9, 5]]]
8 --> [[[1, 9], [4, 7]], [[8, 2], [11, 12]], [[5, 3], [10, 6]]]
9 --> [[[1, 10], [5, 8]], [[9, 3], [12, 2]], [[6, 4], [11, 7]]]
10 --> [[[1, 11], [6, 9]], [[10, 4], [2, 3]], [[7, 5], [12, 8]]]
11 --> [[[1, 12], [7, 10]], [[11, 5], [3, 4]], [[8, 6], [2, 9]]]
==========================================
n=16
1 --> [[[1, 2], [14, 3]], [[11, 4], [9, 15]], [[13, 16], [10, 8]], [[6, 5], [7, 12]]]
2 --> [[[1, 3], [15, 4]], [[12, 5], [10, 16]], [[14, 2], [11, 9]], [[7, 6], [8, 13]]]
3 --> [[[1, 4], [16, 5]], [[13, 6], [11, 2]], [[15, 3], [12, 10]], [[8, 7], [9, 14]]]
4 --> [[[1, 5], [2, 6]], [[14, 7], [12, 3]], [[16, 4], [13, 11]], [[9, 8], [10, 15]]]
5 --> [[[1, 6], [3, 7]], [[15, 8], [13, 4]], [[2, 5], [14, 12]], [[10, 9], [11, 16]]]
6 --> [[[1, 7], [4, 8]], [[16, 9], [14, 5]], [[3, 6], [15, 13]], [[11, 10], [12, 2]]]
7 --> [[[1, 8], [5, 9]], [[2, 10], [15, 6]], [[4, 7], [16, 14]], [[12, 11], [13, 3]]]
8 --> [[[1, 9], [6, 10]], [[3, 11], [16, 7]], [[5, 8], [2, 15]], [[13, 12], [14, 4]]]
9 --> [[[1, 10], [7, 11]], [[4, 12], [2, 8]], [[6, 9], [3, 16]], [[14, 13], [15, 5]]]
10 --> [[[1, 11], [8, 12]], [[5, 13], [3, 9]], [[7, 10], [4, 2]], [[15, 14], [16, 6]]]
11 --> [[[1, 12], [9, 13]], [[6, 14], [4, 10]], [[8, 11], [5, 3]], [[16,15], [2, 7]]]
12 --> [[[1, 13], [10, 14]], [[7, 15], [5, 11]], [[9, 12], [6, 4]], [[2, 16], [3, 8]]]
13 --> [[[1, 14], [11, 15]], [[8, 16], [6, 12]], [[10, 13], [7, 5]], [[3, 2], [4, 9]]]
14 --> [[[1, 15], [12, 16]], [[9, 2], [7, 13]], [[11, 14], [8, 6]], [[4, 3], [5, 10]]]
15 --> [[[1, 16], [13, 2]], [[10, 3], [8, 14]], [[12, 15], [9, 7]], [[5, 4], [6, 11]]]
1 --> [[[1, 2], [8, 15]], [[3, 9], [5, 4]], [[13, 10], [6, 16]], [[14, 12], [7, 11]]]
2 --> [[[1, 3], [9, 16]], [[4, 10], [6, 5]], [[14, 11], [7, 2]], [[15, 13], [8, 12]]]
3 --> [[[1, 4], [10, 2]], [[5, 11], [7, 6]], [[15, 12], [8, 3]], [[16, 14], [9, 13]]]
4 --> [[[1, 5], [11, 3]], [[6, 12], [8, 7]], [[16, 13], [9, 4]], [[2, 15], [10, 14]]]
5 --> [[[1, 6], [12, 4]], [[7, 13], [9, 8]], [[2, 14], [10, 5]], [[3, 16], [11, 15]]]
6 --> [[[1, 7], [13, 5]], [[8, 14], [10, 9]], [[3, 15], [11, 6]], [[4, 2], [12, 16]]]
7 --> [[[1, 8], [14, 6]], [[9, 15], [11, 10]], [[4, 16], [12, 7]], [[5, 3], [13, 2]]]
8 --> [[[1, 9], [15, 7]], [[10, 16], [12, 11]], [[5, 2], [13, 8]], [[6, 4], [14, 3]]]
9 --> [[[1, 10], [16, 8]], [[11, 2], [13, 12]], [[6, 3], [14, 9]], [[7, 5], [15, 4]]]
10 --> [[[1, 11], [2, 9]], [[12, 3], [14, 13]], [[7, 4], [15, 10]], [[8, 6], [16, 5]]]
11 --> [[[1, 12], [3, 10]], [[13, 4], [15, 14]], [[8, 5], [16, 11]], [[9, 7], [2, 6]]]
12 --> [[[1, 13], [4, 11]], [[14, 5], [16, 15]], [[9, 6], [2, 12]], [[10, 8], [3, 7]]]
13 --> [[[1, 14], [5, 12]], [[15, 6], [2, 16]], [[10, 7], [3, 13]], [[11, 9], [4, 8]]]
14 --> [[[1, 15], [6, 13]], [[16, 7], [3, 2]], [[11, 8], [4, 14]], [[12, 10], [5, 9]]]
15 --> [[[1, 16], [7, 14]], [[2, 8], [4, 3]], [[12, 9], [5, 15]], [[13, 11], [6, 10]]]
==========================================
n= 20
1 --> [[[1, 2], [12, 19]], [[3, 5], [13, 18]], [[16, 20], [4, 15]], [[7, 17], [10, 11]], [[6, 9], [8, 14]]]
2 --> [[[1, 3], [13, 20]], [[4, 6], [14, 19]], [[17, 2], [5, 16]], [[8, 18], [11, 12]], [[7, 10], [9, 15]]]
3 --> [[[1, 4], [14, 2]], [[5, 7], [15, 20]], [[18, 3], [6, 17]], [[9, 19], [12, 13]], [[8, 11], [10, 16]]]
4 --> [[[1, 5], [15, 3]], [[6, 8], [16, 2]], [[19, 4], [7, 18]], [[10, 20], [13, 14]], [[9, 12], [11, 17]]]
5 --> [[[1, 6], [16, 4]], [[7, 9], [17, 3]], [[20, 5], [8, 19]], [[11, 2], [14, 15]], [[10, 13], [12, 18]]]
6 --> [[[1, 7], [17, 5]], [[8, 10], [18, 4]], [[2, 6], [9, 20]], [[12, 3], [15, 16]], [[11, 14], [13, 19]]]
7 --> [[[1, 8], [18, 6]], [[9, 11], [19, 5]], [[3, 7], [10, 2]], [[13, 4], [16, 17]], [[12, 15], [14, 20]]]
8 --> [[[1, 9], [19, 7]], [[10, 12], [20, 6]], [[4, 8], [11, 3]], [[14, 5], [17, 18]], [[13, 16], [15, 2]]]
9 --> [[[1, 10], [20, 8]], [[11, 13], [2, 7]], [[5, 9], [12, 4]], [[15, 6], [18, 19]], [[14, 17], [16, 3]]]
10 --> [[[1, 11], [2, 9]], [[12, 14], [3, 8]], [[6, 10], [13, 5]], [[16, 7], [19, 20]], [[15, 18], [17, 4]]]
11 --> [[[1, 12], [3, 10]], [[13, 15], [4, 9]], [[7, 11], [14, 6]], [[17, 8], [20, 2]], [[16, 19], [18, 5]]]
12 --> [[[1, 13], [4, 11]], [[14, 16], [5, 10]], [[8, 12], [15, 7]], [[18, 9], [2, 3]], [[17, 20], [19, 6]]]
13 --> [[[1, 14], [5, 12]], [[15, 17], [6, 11]], [[9, 13], [16, 8]], [[19, 10], [3, 4]], [[18, 2], [20, 7]]]
14 --> [[[1, 15], [6, 13]], [[16, 18], [7, 12]], [[10, 14], [17, 9]], [[20, 11], [4, 5]], [[19, 3], [2, 8]]]
15 --> [[[1, 16], [7, 14]], [[17, 19], [8, 13]], [[11, 15], [18, 10]], [[2, 12], [5, 6]], [[20, 4], [3, 9]]]
16 --> [[[1, 17], [8, 15]], [[18, 20], [9, 14]], [[12, 16], [19, 11]], [[3, 13], [6, 7]], [[2, 5], [4, 10]]]
17 --> [[[1, 18], [9, 16]], [[19, 2], [10, 15]], [[13, 17], [20, 12]], [[4, 14], [7, 8]], [[3, 6], [5, 11]]]
18 --> [[[1, 19], [10, 17]], [[20, 3], [11, 16]], [[14, 18], [2, 13]], [[5, 15], [8, 9]], [[4, 7], [6, 12]]]
19 --> [[[1, 20], [11, 18]], [[2, 4], [12, 17]], [[15, 19], [3, 14]], [[6, 16], [9, 10]], [[5, 8], [7, 13]]]
==========================================
Par ailleurs, Alain Esculier et Rober Ferréol mentionnent le site
http://www.durangobill.com/BridgeCyclicSolutions.html qui recense les solutions pour organiser un tournoi de bridge comportant jusqu’à 19 tables (76 joueurs) selon les mêmes principes que le tournoi de belote : chaque joueur a les n-1 autres concurrents une fois comme coéquipier et deux fois comme adversaire.
Ces solutions ont, semble-t-il, été trouvées par ordinateur. Aucune méthode de construction générale n'est donnée pour trouver le premier tour d'un tel tournoi.
Selon les notations précédemment utilisées par Alain Esculier, elles se présentent comme suit :
============tournoi à 76 joueurs de Durango===========
1 --> [[[1, 76], [13, 31]], [[2, 39], [12, 43]], [[74, 75], [21, 23]], [[58, 61], [60, 64]], [[57, 62], [53, 67]], [[18, 24], [25, 48]], [[19, 26], [5, 37]], [[65, 73], [30, 50]], [[63, 72], [8, 35]], [[56, 66], [16, 27]], [[59, 71], [15, 44]], [[55, 68], [6, 36]], [[14, 29], [22, 47]], [[54, 70], [7, 41]], [[52, 69], [3, 38]], [[32, 51], [10, 34]], [[28, 49], [11, 33]], [[20, 46], [4, 40]], [[17, 45], [9, 42]]]
2 --> [[[1, 75], [12, 30]], [[76, 38], [11, 42]], [[73, 74], [20, 22]], [[57, 60], [59, 63]], [[56, 61], [52, 66]], [[17, 23], [24, 47]], [[18, 25], [4, 36]], [[64, 72], [29, 49]], [[62, 71], [7, 34]], [[55, 65], [15, 26]], [[58, 70], [14, 43]], [[54, 67], [5, 35]], [[13, 28], [21, 46]], [[53, 69], [6, 40]], [[51, 68], [2, 37]], [[31, 50], [9, 33]], [[27, 48], [10, 32]], [[19, 45], [3, 39]], [[16, 44], [8, 41]]]
3 --> [[[1, 74], [11, 29]], [[75, 37], [10, 41]], [[72, 73], [19, 21]], [[56, 59], [58, 62]], [[55, 60], [51, 65]], [[16, 22], [23, 46]], [[17, 24], [3, 35]], [[63, 71], [28, 48]], [[61, 70], [6, 33]], [[54, 64], [14, 25]], [[57, 69], [13, 42]], [[53, 66], [4, 34]], [[12, 27], [20, 45]], [[52, 68], [5, 39]], [[50, 67], [76, 36]], [[30, 49], [8, 32]], [[26, 47], [9, 31]], [[18, 44], [2, 38]], [[15, 43], [7, 40]]]
4 --> [[[1, 73], [10, 28]], [[74, 36], [9, 40]], [[71, 72], [18, 20]], [[55, 58], [57, 61]], [[54, 59], [50, 64]], [[15, 21], [22, 45]], [[16, 23], [2, 34]], [[62, 70], [27, 47]], [[60, 69], [5, 32]], [[53, 63], [13, 24]], [[56, 68], [12, 41]], [[52, 65], [3, 33]], [[11, 26], [19, 44]], [[51, 67], [4, 38]], [[49, 66], [75, 35]], [[29, 48], [7, 31]], [[25, 46], [8, 30]], [[17, 43], [76, 37]], [[14, 42], [6, 39]]]
5 --> [[[1, 72], [9, 27]], [[73, 35], [8, 39]], [[70, 71], [17, 19]], [[54, 57], [56, 60]], [[53, 58], [49, 63]], [[14, 20], [21, 44]], [[15, 22], [76, 33]], [[61, 69], [26, 46]], [[59, 68], [4, 31]], [[52, 62], [12, 23]], [[55, 67], [11, 40]], [[51, 64], [2, 32]], [[10, 25], [18, 43]], [[50, 66], [3, 37]], [[48, 65], [74, 34]], [[28, 47], [6, 30]], [[24, 45], [7, 29]], [[16, 42], [75, 36]], [[13, 41], [5, 38]]]
6 --> [[[1, 71], [8, 26]], [[72, 34], [7, 38]], [[69, 70], [16, 18]], [[53, 56], [55, 59]], [[52, 57], [48, 62]], [[13, 19], [20, 43]], [[14, 21], [75, 32]], [[60, 68], [25, 45]], [[58, 67], [3, 30]], [[51, 61], [11, 22]], [[54, 66], [10, 39]], [[50, 63], [76, 31]], [[9, 24], [17, 42]], [[49, 65], [2, 36]], [[47, 64], [73, 33]], [[27, 46], [5, 29]], [[23, 44], [6, 28]], [[15, 41], [74, 35]], [[12, 40], [4, 37]]]
7 --> [[[1, 70], [7, 25]], [[71, 33], [6, 37]], [[68, 69], [15, 17]], [[52, 55], [54, 58]], [[51, 56], [47, 61]], [[12, 18], [19, 42]], [[13, 20], [74, 31]], [[59, 67], [24, 44]], [[57, 66], [2, 29]], [[50, 60], [10, 21]], [[53, 65], [9, 38]], [[49, 62], [75, 30]], [[8, 23], [16, 41]], [[48, 64], [76, 35]],
[[46, 63], [72, 32]], [[26, 45], [4, 28]], [[22, 43], [5, 27]], [[14, 40], [73, 34]], [[11, 39], [3, 36]]]
8 --> [[[1, 69], [6, 24]], [[70, 32], [5, 36]], [[67, 68], [14, 16]], [[51, 54], [53, 57]], [[50, 55], [46, 60]], [[11, 17], [18, 41]], [[12, 19], [73, 30]], [[58, 66], [23, 43]], [[56, 65], [76, 28]], [[49, 59], [9, 20]], [[52, 64], [8, 37]], [[48, 61], [74, 29]], [[7, 22], [15, 40]], [[47, 63], [75, 34]], [[45, 62], [71, 31]], [[25, 44], [3, 27]], [[21, 42], [4, 26]], [[13, 39], [72, 33]], [[10, 38], [2, 35]]]
9 --> [[[1, 68], [5, 23]], [[69, 31], [4, 35]], [[66, 67], [13, 15]], [[50, 53], [52, 56]], [[49, 54], [45, 59]], [[10, 16], [17, 40]], [[11, 18], [72, 29]], [[57, 65], [22, 42]], [[55, 64], [75, 27]], [[48, 58], [8, 19]], [[51, 63], [7, 36]], [[47, 60], [73, 28]], [[6, 21], [14, 39]], [[46, 62], [74, 33]], [[44, 61], [70, 30]], [[24, 43], [2, 26]], [[20, 41], [3, 25]], [[12, 38], [71, 32]], [[9, 37], [76, 34]]]
10 --> [[[1, 67], [4, 22]], [[68, 30], [3, 34]], [[65, 66], [12, 14]], [[49, 52], [51, 55]], [[48, 53], [44, 58]], [[9, 15], [16, 39]], [[10, 17], [71, 28]], [[56, 64], [21, 41]], [[54, 63], [74, 26]], [[47, 57], [7, 18]], [[50, 62], [6, 35]], [[46, 59], [72, 27]], [[5, 20], [13, 38]], [[45, 61], [73, 32]], [[43, 60], [69, 29]], [[23, 42], [76, 25]], [[19, 40], [2, 24]], [[11, 37], [70, 31]], [[8, 36], [75, 33]]]
11 --> [[[1, 66], [3, 21]], [[67, 29], [2, 33]], [[64, 65], [11, 13]], [[48, 51], [50, 54]], [[47, 52], [43, 57]], [[8, 14], [15, 38]], [[9, 16], [70, 27]], [[55, 63], [20, 40]], [[53, 62], [73, 25]], [[46, 56], [6, 17]], [[49, 61], [5, 34]], [[45, 58], [71, 26]], [[4, 19], [12, 37]], [[44, 60], [72, 31]], [[42, 59], [68, 28]], [[22, 41], [75, 24]], [[18, 39], [76, 23]], [[10, 36], [69, 30]], [[7, 35], [74, 32]]]
12 --> [[[1, 65], [2, 20]], [[66, 28], [76, 32]], [[63, 64], [10, 12]], [[47, 50], [49, 53]], [[46, 51], [42, 56]], [[7, 13], [14, 37]], [[8, 15], [69, 26]], [[54, 62], [19, 39]], [[52, 61], [72, 24]], [[45, 55], [5, 16]], [[48, 60], [4, 33]], [[44, 57], [70, 25]], [[3, 18], [11, 36]], [[43, 59], [71, 30]], [[41, 58], [67, 27]], [[21, 40], [74, 23]], [[17, 38], [75, 22]], [[9, 35], [68, 29]], [[6, 34], [73, 31]]]
13 --> [[[1, 64], [76, 19]], [[65, 27], [75, 31]], [[62, 63], [9, 11]], [[46, 49], [48, 52]], [[45, 50], [41, 55]], [[6, 12], [13, 36]], [[7, 14], [68, 25]], [[53, 61], [18, 38]], [[51, 60], [71, 23]], [[44, 54], [4, 15]], [[47, 59], [3, 32]], [[43, 56], [69, 24]], [[2, 17], [10, 35]], [[42, 58], [70, 29]], [[40, 57], [66, 26]], [[20, 39], [73, 22]], [[16, 37], [74, 21]], [[8, 34], [67, 28]], [[5, 33], [72, 30]]]
14 --> [[[1, 63], [75, 18]], [[64, 26], [74, 30]], [[61, 62], [8, 10]], [[45, 48], [47, 51]], [[44, 49], [40, 54]], [[5, 11], [12, 35]], [[6, 13], [67, 24]], [[52, 60], [17, 37]], [[50, 59], [70, 22]], [[43, 53], [3, 14]], [[46, 58], [2, 31]], [[42, 55], [68, 23]], [[76, 16], [9, 34]], [[41, 57], [69, 28]], [[39, 56], [65, 25]], [[19, 38], [72, 21]], [[15, 36], [73, 20]], [[7, 33], [66, 27]], [[4, 32], [71, 29]]]
15 --> [[[1, 62], [74, 17]], [[63, 25], [73, 29]], [[60, 61], [7, 9]], [[44, 47], [46, 50]], [[43, 48], [39, 53]], [[4, 10], [11, 34]], [[5, 12], [66, 23]], [[51, 59], [16, 36]], [[49, 58], [69, 21]], [[42, 52], [2, 13]], [[45, 57], [76, 30]], [[41, 54], [67, 22]], [[75, 15], [8, 33]], [[40, 56], [68, 27]], [[38, 55], [64, 24]], [[18, 37], [71, 20]], [[14, 35], [72, 19]], [[6, 32], [65, 26]], [[3, 31], [70, 28]]]
16 --> [[[1, 61], [73, 16]], [[62, 24], [72, 28]], [[59, 60], [6, 8]], [[43, 46], [45, 49]], [[42, 47], [38, 52]], [[3, 9], [10, 33]], [[4, 11], [65, 22]], [[50, 58], [15, 35]], [[48, 57], [68, 20]], [[41, 51], [76, 12]], [[44, 56], [75, 29]], [[40, 53], [66, 21]], [[74, 14], [7, 32]], [[39, 55], [67, 26]], [[37, 54], [63, 23]], [[17, 36], [70, 19]], [[13, 34], [71, 18]], [[5, 31], [64, 25]], [[2, 30], [69, 27]]]
17 --> [[[1, 60], [72, 15]], [[61, 23], [71, 27]], [[58, 59], [5, 7]], [[42, 45], [44, 48]], [[41, 46], [37, 51]], [[2, 8], [9, 32]], [[3, 10], [64, 21]], [[49, 57], [14, 34]], [[47, 56], [67, 19]], [[40, 50], [75, 11]], [[43, 55], [74, 28]], [[39, 52], [65, 20]], [[73, 13], [6, 31]], [[38, 54], [66, 25]], [[36, 53], [62, 22]], [[16, 35], [69, 18]], [[12, 33], [70, 17]], [[4, 30], [63, 24]], [[76, 29], [68, 26]]]
18 --> [[[1, 59], [71, 14]], [[60, 22], [70, 26]], [[57, 58], [4, 6]], [[41, 44], [43, 47]], [[40, 45], [36, 50]], [[76, 7], [8, 31]], [[2, 9], [63, 20]], [[48, 56], [13, 33]], [[46, 55], [66, 18]], [[39, 49], [74, 10]], [[42, 54], [73, 27]], [[38, 51], [64, 19]], [[72, 12], [5, 30]], [[37, 53], [65, 24]], [[35, 52], [61, 21]], [[15, 34], [68, 17]], [[11, 32], [69, 16]], [[3, 29], [62, 23]], [[75, 28], [67, 25]]]
19 --> [[[1, 58], [70, 13]], [[59, 21], [69, 25]], [[56, 57], [3, 5]], [[40, 43], [42, 46]], [[39, 44], [35, 49]], [[75, 6], [7, 30]], [[76, 8], [62, 19]], [[47, 55], [12, 32]], [[45, 54], [65, 17]], [[38, 48], [73, 9]], [[41, 53], [72, 26]], [[37, 50], [63, 18]], [[71, 11], [4, 29]], [[36, 52], [64, 23]], [[34, 51], [60, 20]], [[14, 33], [67, 16]], [[10, 31], [68, 15]], [[2, 28], [61, 22]], [[74, 27], [66, 24]]]
20 --> [[[1, 57], [69, 12]], [[58, 20], [68, 24]], [[55, 56], [2, 4]], [[39, 42], [41, 45]], [[38, 43], [34, 48]], [[74, 5], [6, 29]], [[75, 7], [61, 18]], [[46, 54], [11, 31]], [[44, 53], [64, 16]], [[37, 47], [72, 8]], [[40, 52], [71, 25]], [[36, 49], [62, 17]], [[70, 10], [3, 28]], [[35, 51], [63, 22]], [[33, 50], [59, 19]], [[13, 32], [66, 15]], [[9, 30], [67, 14]], [[76, 27], [60, 21]], [[73, 26], [65, 23]]]
21 --> [[[1, 56], [68, 11]], [[57, 19], [67, 23]], [[54, 55], [76, 3]], [[38, 41], [40, 44]], [[37, 42], [33, 47]], [[73, 4], [5, 28]], [[74, 6], [60, 17]], [[45, 53], [10, 30]], [[43, 52], [63, 15]], [[36, 46], [71, 7]], [[39, 51], [70, 24]], [[35, 48], [61, 16]], [[69, 9], [2, 27]], [[34, 50], [62, 21]], [[32, 49], [58, 18]], [[12, 31], [65, 14]], [[8, 29], [66, 13]], [[75, 26], [59, 20]], [[72, 25], [64, 22]]]
22 --> [[[1, 55], [67, 10]], [[56, 18], [66, 22]], [[53, 54], [75, 2]], [[37, 40], [39, 43]], [[36, 41], [32, 46]], [[72, 3], [4, 27]], [[73, 5], [59, 16]], [[44, 52], [9, 29]], [[42, 51], [62, 14]], [[35, 45], [70, 6]], [[38, 50], [69, 23]], [[34, 47], [60, 15]], [[68, 8], [76, 26]], [[33, 49], [61, 20]], [[31, 48], [57, 17]], [[11, 30], [64, 13]], [[7, 28], [65, 12]], [[74, 25], [58, 19]], [[71, 24], [63, 21]]]
23 --> [[[1, 54], [66, 9]], [[55, 17], [65, 21]], [[52, 53], [74, 76]], [[36, 39], [38, 42]], [[35, 40], [31, 45]], [[71, 2], [3, 26]], [[72, 4], [58, 15]], [[43, 51], [8, 28]], [[41, 50], [61, 13]], [[34, 44], [69, 5]], [[37, 49], [68, 22]], [[33, 46], [59, 14]], [[67, 7], [75, 25]], [[32, 48], [60, 19]], [[30, 47], [56, 16]], [[10, 29], [63, 12]], [[6, 27], [64, 11]], [[73, 24], [57, 18]], [[70, 23], [62, 20]]]
24 --> [[[1, 53], [65, 8]], [[54, 16], [64, 20]], [[51, 52], [73, 75]], [[35, 38], [37, 41]], [[34, 39], [30, 44]], [[70, 76], [2, 25]], [[71, 3], [57, 14]], [[42, 50], [7, 27]], [[40, 49], [60, 12]], [[33, 43], [68, 4]], [[36, 48], [67, 21]], [[32, 45], [58, 13]], [[66, 6], [74, 24]], [[31, 47], [59,
18]], [[29, 46], [55, 15]], [[9, 28], [62, 11]], [[5, 26], [63, 10]], [[72, 23], [56, 17]], [[69, 22], [61, 19]]]
25 --> [[[1, 52], [64, 7]], [[53, 15], [63, 19]], [[50, 51], [72, 74]], [[34, 37], [36, 40]], [[33, 38], [29, 43]], [[69, 75], [76, 24]], [[70, 2], [56, 13]], [[41, 49], [6, 26]], [[39, 48], [59, 11]], [[32, 42], [67, 3]], [[35, 47], [66, 20]], [[31, 44], [57, 12]], [[65, 5], [73, 23]], [[30, 46], [58, 17]], [[28, 45], [54, 14]], [[8, 27], [61, 10]], [[4, 25], [62, 9]], [[71, 22], [55, 16]], [[68, 21], [60, 18]]]
26 --> [[[1, 51], [63, 6]], [[52, 14], [62, 18]], [[49, 50], [71, 73]], [[33, 36], [35, 39]], [[32, 37], [28, 42]], [[68, 74], [75, 23]], [[69, 76], [55, 12]], [[40, 48], [5, 25]], [[38, 47], [58, 10]], [[31, 41], [66, 2]], [[34, 46], [65, 19]], [[30, 43], [56, 11]], [[64, 4], [72, 22]], [[29, 45], [57, 16]], [[27, 44], [53, 13]], [[7, 26], [60, 9]], [[3, 24], [61, 8]], [[70, 21], [54, 15]], [[67, 20], [59, 17]]]
27 --> [[[1, 50], [62, 5]], [[51, 13], [61, 17]], [[48, 49], [70, 72]], [[32, 35], [34, 38]], [[31, 36], [27, 41]], [[67, 73], [74, 22]], [[68, 75], [54, 11]], [[39, 47], [4, 24]], [[37, 46], [57, 9]], [[30, 40], [65, 76]], [[33, 45], [64, 18]], [[29, 42], [55, 10]], [[63, 3], [71, 21]], [[28, 44], [56, 15]], [[26, 43], [52, 12]], [[6, 25], [59, 8]], [[2, 23], [60, 7]], [[69, 20], [53, 14]], [[66, 19], [58, 16]]]
28 --> [[[1, 49], [61, 4]], [[50, 12], [60, 16]], [[47, 48], [69, 71]], [[31, 34], [33, 37]], [[30, 35], [26, 40]], [[66, 72], [73, 21]], [[67, 74], [53, 10]], [[38, 46], [3, 23]], [[36, 45], [56, 8]], [[29, 39], [64, 75]], [[32, 44], [63, 17]], [[28, 41], [54, 9]], [[62, 2], [70, 20]], [[27, 43], [55, 14]], [[25, 42], [51, 11]], [[5, 24], [58, 7]], [[76, 22], [59, 6]], [[68, 19], [52, 13]], [[65, 18], [57, 15]]]
29 --> [[[1, 48], [60, 3]], [[49, 11], [59, 15]], [[46, 47], [68, 70]], [[30, 33], [32, 36]], [[29, 34], [25, 39]], [[65, 71], [72, 20]], [[66, 73], [52, 9]], [[37, 45], [2, 22]], [[35, 44], [55, 7]], [[28, 38], [63, 74]], [[31, 43], [62, 16]], [[27, 40], [53, 8]], [[61, 76], [69, 19]], [[26, 42], [54, 13]], [[24, 41], [50, 10]], [[4, 23], [57, 6]], [[75, 21], [58, 5]], [[67, 18], [51, 12]], [[64, 17], [56, 14]]]
30 --> [[[1, 47], [59, 2]], [[48, 10], [58, 14]], [[45, 46], [67, 69]], [[29, 32], [31, 35]], [[28, 33], [24, 38]], [[64, 70], [71, 19]], [[65, 72], [51, 8]], [[36, 44], [76, 21]], [[34, 43], [54, 6]], [[27, 37], [62, 73]], [[30, 42], [61, 15]], [[26, 39], [52, 7]], [[60, 75], [68, 18]], [[25, 41], [53, 12]], [[23, 40], [49, 9]], [[3, 22], [56, 5]], [[74, 20], [57, 4]], [[66, 17], [50, 11]], [[63, 16], [55, 13]]]
31 --> [[[1, 46], [58, 76]], [[47, 9], [57, 13]], [[44, 45], [66, 68]], [[28, 31], [30, 34]], [[27, 32], [23, 37]], [[63, 69], [70, 18]], [[64, 71], [50, 7]], [[35, 43], [75, 20]], [[33, 42], [53, 5]], [[26, 36], [61, 72]], [[29, 41], [60, 14]], [[25, 38], [51, 6]], [[59, 74], [67, 17]], [[24, 40], [52, 11]], [[22, 39], [48, 8]], [[2, 21], [55, 4]], [[73, 19], [56, 3]], [[65, 16], [49, 10]], [[62, 15], [54, 12]]]
32 --> [[[1, 45], [57, 75]], [[46, 8], [56, 12]], [[43, 44], [65, 67]], [[27, 30], [29, 33]], [[26, 31], [22, 36]], [[62, 68], [69, 17]], [[63, 70], [49, 6]], [[34, 42], [74, 19]], [[32, 41], [52, 4]], [[25, 35], [60, 71]], [[28, 40], [59, 13]], [[24, 37], [50, 5]], [[58, 73], [66, 16]], [[23, 39], [51, 10]], [[21, 38], [47, 7]], [[76, 20], [54, 3]], [[72, 18], [55, 2]], [[64, 15], [48, 9]], [[61, 14], [53, 11]]]
33 --> [[[1, 44], [56, 74]], [[45, 7], [55, 11]], [[42, 43], [64, 66]], [[26, 29], [28, 32]], [[25, 30], [21, 35]], [[61, 67], [68, 16]], [[62, 69], [48, 5]], [[33, 41], [73, 18]], [[31, 40], [51, 3]], [[24, 34], [59, 70]], [[27, 39], [58, 12]], [[23, 36], [49, 4]], [[57, 72], [65, 15]], [[22, 38], [50, 9]], [[20, 37], [46, 6]], [[75, 19], [53, 2]], [[71, 17], [54, 76]], [[63, 14], [47, 8]], [[60, 13], [52, 10]]]
34 --> [[[1, 43], [55, 73]], [[44, 6], [54, 10]], [[41, 42], [63, 65]], [[25, 28], [27, 31]], [[24, 29], [20, 34]], [[60, 66], [67, 15]], [[61, 68], [47, 4]], [[32, 40], [72, 17]], [[30, 39], [50, 2]], [[23, 33], [58, 69]], [[26, 38], [57, 11]], [[22, 35], [48, 3]], [[56, 71], [64, 14]], [[21, 37], [49, 8]], [[19, 36], [45, 5]], [[74, 18], [52, 76]], [[70, 16], [53, 75]], [[62, 13], [46, 7]], [[59, 12], [51, 9]]]
35 --> [[[1, 42], [54, 72]], [[43, 5], [53, 9]], [[40, 41], [62, 64]], [[24, 27], [26, 30]], [[23, 28], [19, 33]], [[59, 65], [66, 14]], [[60, 67], [46, 3]], [[31, 39], [71, 16]], [[29, 38], [49, 76]], [[22, 32], [57, 68]], [[25, 37], [56, 10]], [[21, 34], [47, 2]], [[55, 70], [63, 13]], [[20, 36], [48, 7]], [[18, 35], [44, 4]], [[73, 17], [51, 75]], [[69, 15], [52, 74]], [[61, 12], [45, 6]], [[58, 11], [50, 8]]]
36 --> [[[1, 41], [53, 71]], [[42, 4], [52, 8]], [[39, 40], [61, 63]], [[23, 26], [25, 29]], [[22, 27], [18, 32]], [[58, 64], [65, 13]], [[59, 66], [45, 2]], [[30, 38], [70, 15]], [[28, 37], [48, 75]], [[21, 31], [56, 67]], [[24, 36], [55, 9]], [[20, 33], [46, 76]], [[54, 69], [62, 12]], [[19, 35], [47, 6]], [[17, 34], [43, 3]], [[72, 16], [50, 74]], [[68, 14], [51, 73]], [[60, 11], [44, 5]], [[57, 10], [49, 7]]]
37 --> [[[1, 40], [52, 70]], [[41, 3], [51, 7]], [[38, 39], [60, 62]], [[22, 25], [24, 28]], [[21, 26], [17, 31]], [[57, 63], [64, 12]], [[58, 65], [44, 76]], [[29, 37], [69, 14]], [[27, 36], [47, 74]], [[20, 30], [55, 66]], [[23, 35], [54, 8]], [[19, 32], [45, 75]], [[53, 68], [61, 11]], [[18, 34], [46, 5]], [[16, 33], [42, 2]], [[71, 15], [49, 73]], [[67, 13], [50, 72]], [[59, 10], [43, 4]], [[56, 9], [48, 6]]]
38 --> [[[1, 39], [51, 69]], [[40, 2], [50, 6]], [[37, 38], [59, 61]], [[21, 24], [23, 27]], [[20, 25], [16, 30]], [[56, 62], [63, 11]], [[57, 64], [43, 75]], [[28, 36], [68, 13]], [[26, 35], [46, 73]], [[19, 29], [54, 65]], [[22, 34], [53, 7]], [[18, 31], [44, 74]], [[52, 67], [60, 10]], [[17, 33], [45, 4]], [[15, 32], [41, 76]], [[70, 14], [48, 72]], [[66, 12], [49, 71]], [[58, 9], [42, 3]], [[55, 8], [47, 5]]]
39 --> [[[1, 38], [50, 68]], [[39, 76], [49, 5]], [[36, 37], [58, 60]], [[20, 23], [22, 26]], [[19, 24], [15, 29]], [[55, 61], [62, 10]], [[56, 63], [42, 74]], [[27, 35], [67, 12]], [[25, 34], [45, 72]], [[18, 28], [53, 64]], [[21, 33], [52, 6]], [[17, 30], [43, 73]], [[51, 66], [59, 9]], [[16, 32], [44, 3]], [[14, 31], [40, 75]], [[69, 13], [47, 71]], [[65, 11], [48, 70]], [[57, 8], [41, 2]], [[54, 7], [46, 4]]]
40 --> [[[1, 37], [49, 67]], [[38, 75], [48, 4]], [[35, 36], [57, 59]], [[19, 22], [21, 25]], [[18, 23], [14, 28]], [[54, 60], [61, 9]], [[55, 62], [41, 73]], [[26, 34], [66, 11]], [[24, 33], [44, 71]], [[17, 27], [52, 63]], [[20, 32], [51, 5]], [[16, 29], [42, 72]], [[50, 65], [58, 8]], [[15, 31], [43, 2]], [[13, 30], [39, 74]], [[68, 12], [46, 70]], [[64, 10], [47, 69]], [[56, 7], [40, 76]], [[53, 6], [45, 3]]]
41 --> [[[1, 36], [48, 66]], [[37, 74], [47, 3]], [[34, 35], [56, 58]], [[18, 21], [20, 24]], [[17,
22], [13, 27]], [[53, 59], [60, 8]], [[54, 61], [40, 72]], [[25, 33], [65, 10]], [[23, 32], [43, 70]], [[16, 26], [51, 62]], [[19, 31], [50, 4]], [[15, 28], [41, 71]], [[49, 64], [57, 7]], [[14, 30], [42, 76]], [[12, 29], [38, 73]], [[67, 11], [45, 69]], [[63, 9], [46, 68]], [[55, 6], [39, 75]], [[52, 5], [44, 2]]]
42 --> [[[1, 35], [47, 65]], [[36, 73], [46, 2]], [[33, 34], [55, 57]], [[17, 20], [19, 23]], [[16, 21], [12, 26]], [[52, 58], [59, 7]], [[53, 60], [39, 71]], [[24, 32], [64, 9]], [[22, 31], [42, 69]], [[15, 25], [50, 61]], [[18, 30], [49, 3]], [[14, 27], [40, 70]], [[48, 63], [56, 6]], [[13, 29], [41, 75]], [[11, 28], [37, 72]], [[66, 10], [44, 68]], [[62, 8], [45, 67]], [[54, 5], [38, 74]], [[51, 4], [43, 76]]]
43 --> [[[1, 34], [46, 64]], [[35, 72], [45, 76]], [[32, 33], [54, 56]], [[16, 19], [18, 22]], [[15, 20], [11, 25]], [[51, 57], [58, 6]], [[52, 59], [38, 70]], [[23, 31], [63, 8]], [[21, 30], [41, 68]], [[14, 24], [49, 60]], [[17, 29], [48, 2]], [[13, 26], [39, 69]], [[47, 62], [55, 5]], [[12, 28], [40, 74]], [[10, 27], [36, 71]], [[65, 9], [43, 67]], [[61, 7], [44, 66]], [[53, 4], [37, 73]], [[50, 3], [42, 75]]]
44 --> [[[1, 33], [45, 63]], [[34, 71], [44, 75]], [[31, 32], [53, 55]], [[15, 18], [17, 21]], [[14, 19], [10, 24]], [[50, 56], [57, 5]], [[51, 58], [37, 69]], [[22, 30], [62, 7]], [[20, 29], [40, 67]], [[13, 23], [48, 59]], [[16, 28], [47, 76]], [[12, 25], [38, 68]], [[46, 61], [54, 4]], [[11, 27], [39, 73]], [[9, 26], [35, 70]], [[64, 8], [42, 66]], [[60, 6], [43, 65]], [[52, 3], [36, 72]], [[49, 2], [41, 74]]]
45 --> [[[1, 32], [44, 62]], [[33, 70], [43, 74]], [[30, 31], [52, 54]], [[14, 17], [16, 20]], [[13, 18], [9, 23]], [[49, 55], [56, 4]], [[50, 57], [36, 68]], [[21, 29], [61, 6]], [[19, 28], [39, 66]], [[12, 22], [47, 58]], [[15, 27], [46, 75]], [[11, 24], [37, 67]], [[45, 60], [53, 3]], [[10, 26], [38, 72]], [[8, 25], [34, 69]], [[63, 7], [41, 65]], [[59, 5], [42, 64]], [[51, 2], [35, 71]], [[48, 76], [40, 73]]]
46 --> [[[1, 31], [43, 61]], [[32, 69], [42, 73]], [[29, 30], [51, 53]], [[13, 16], [15, 19]], [[12, 17], [8, 22]], [[48, 54], [55, 3]], [[49, 56], [35, 67]], [[20, 28], [60, 5]], [[18, 27], [38, 65]], [[11, 21], [46, 57]], [[14, 26], [45, 74]], [[10, 23], [36, 66]], [[44, 59], [52, 2]], [[9, 25], [37, 71]], [[7, 24], [33, 68]], [[62, 6], [40, 64]], [[58, 4], [41, 63]], [[50, 76], [34, 70]], [[47, 75], [39, 72]]]
47 --> [[[1, 30], [42, 60]], [[31, 68], [41, 72]], [[28, 29], [50, 52]], [[12, 15], [14, 18]], [[11, 16], [7, 21]], [[47, 53], [54, 2]], [[48, 55], [34, 66]], [[19, 27], [59, 4]], [[17, 26], [37, 64]], [[10, 20], [45, 56]], [[13, 25], [44, 73]], [[9, 22], [35, 65]], [[43, 58], [51, 76]], [[8, 24], [36, 70]], [[6, 23], [32, 67]], [[61, 5], [39, 63]], [[57, 3], [40, 62]], [[49, 75], [33, 69]], [[46, 74], [38, 71]]]
48 --> [[[1, 29], [41, 59]], [[30, 67], [40, 71]], [[27, 28], [49, 51]], [[11, 14], [13, 17]], [[10, 15], [6, 20]], [[46, 52], [53, 76]], [[47, 54], [33, 65]], [[18, 26], [58, 3]], [[16, 25], [36, 63]], [[9, 19], [44, 55]], [[12, 24], [43, 72]], [[8, 21], [34, 64]], [[42, 57], [50, 75]], [[7, 23], [35, 69]], [[5, 22], [31, 66]], [[60, 4], [38, 62]], [[56, 2], [39, 61]], [[48, 74], [32, 68]], [[45, 73], [37, 70]]]
49 --> [[[1, 28], [40, 58]], [[29, 66], [39, 70]], [[26, 27], [48, 50]], [[10, 13], [12, 16]], [[9, 14], [5, 19]], [[45, 51], [52, 75]], [[46, 53], [32, 64]], [[17, 25], [57, 2]], [[15, 24], [35, 62]], [[8, 18], [43, 54]], [[11, 23], [42, 71]], [[7, 20], [33, 63]], [[41, 56], [49, 74]], [[6, 22], [34,
68]], [[4, 21], [30, 65]], [[59, 3], [37, 61]], [[55, 76], [38, 60]], [[47, 73], [31, 67]], [[44, 72], [36, 69]]]
50 --> [[[1, 27], [39, 57]], [[28, 65], [38, 69]], [[25, 26], [47, 49]], [[9, 12], [11, 15]], [[8, 13], [4, 18]], [[44, 50], [51, 74]], [[45, 52], [31, 63]], [[16, 24], [56, 76]], [[14, 23], [34, 61]], [[7, 17], [42, 53]], [[10, 22], [41, 70]], [[6, 19], [32, 62]], [[40, 55], [48, 73]], [[5, 21], [33, 67]], [[3, 20], [29, 64]], [[58, 2], [36, 60]], [[54, 75], [37, 59]], [[46, 72], [30, 66]], [[43, 71], [35, 68]]]
51 --> [[[1, 26], [38, 56]], [[27, 64], [37, 68]], [[24, 25], [46, 48]], [[8, 11], [10, 14]], [[7, 12], [3, 17]], [[43, 49], [50, 73]], [[44, 51], [30, 62]], [[15, 23], [55, 75]], [[13, 22], [33, 60]], [[6, 16], [41, 52]], [[9, 21], [40, 69]], [[5, 18], [31, 61]], [[39, 54], [47, 72]], [[4, 20], [32, 66]], [[2, 19], [28, 63]], [[57, 76], [35, 59]], [[53, 74], [36, 58]], [[45, 71], [29, 65]], [[42, 70], [34, 67]]]
52 --> [[[1, 25], [37, 55]], [[26, 63], [36, 67]], [[23, 24], [45, 47]], [[7, 10], [9, 13]], [[6, 11], [2, 16]], [[42, 48], [49, 72]], [[43, 50], [29, 61]], [[14, 22], [54, 74]], [[12, 21], [32, 59]], [[5, 15], [40, 51]], [[8, 20], [39, 68]], [[4, 17], [30, 60]], [[38, 53], [46, 71]], [[3, 19], [31, 65]], [[76, 18], [27, 62]], [[56, 75], [34, 58]], [[52, 73], [35, 57]], [[44, 70], [28, 64]], [[41, 69], [33, 66]]]
53 --> [[[1, 24], [36, 54]], [[25, 62], [35, 66]], [[22, 23], [44, 46]], [[6, 9], [8, 12]], [[5, 10], [76, 15]], [[41, 47], [48, 71]], [[42, 49], [28, 60]], [[13, 21], [53, 73]], [[11, 20], [31, 58]], [[4, 14], [39, 50]], [[7, 19], [38, 67]], [[3, 16], [29, 59]], [[37, 52], [45, 70]], [[2, 18], [30, 64]], [[75, 17], [26, 61]], [[55, 74], [33, 57]], [[51, 72], [34, 56]], [[43, 69], [27, 63]], [[40, 68], [32, 65]]]
54 --> [[[1, 23], [35, 53]], [[24, 61], [34, 65]], [[21, 22], [43, 45]], [[5, 8], [7, 11]], [[4, 9], [75, 14]], [[40, 46], [47, 70]], [[41, 48], [27, 59]], [[12, 20], [52, 72]], [[10, 19], [30, 57]], [[3, 13], [38, 49]], [[6, 18], [37, 66]], [[2, 15], [28, 58]], [[36, 51], [44, 69]], [[76, 17], [29, 63]], [[74, 16], [25, 60]], [[54, 73], [32, 56]], [[50, 71], [33, 55]], [[42, 68], [26, 62]], [[39, 67], [31, 64]]]
55 --> [[[1, 22], [34, 52]], [[23, 60], [33, 64]], [[20, 21], [42, 44]], [[4, 7], [6, 10]], [[3, 8], [74, 13]], [[39, 45], [46, 69]], [[40, 47], [26, 58]], [[11, 19], [51, 71]], [[9, 18], [29, 56]], [[2, 12], [37, 48]], [[5, 17], [36, 65]], [[76, 14], [27, 57]], [[35, 50], [43, 68]], [[75, 16], [28, 62]], [[73, 15], [24, 59]], [[53, 72], [31, 55]], [[49, 70], [32, 54]], [[41, 67], [25, 61]], [[38, 66], [30, 63]]]
56 --> [[[1, 21], [33, 51]], [[22, 59], [32, 63]], [[19, 20], [41, 43]], [[3, 6], [5, 9]], [[2, 7], [73, 12]], [[38, 44], [45, 68]], [[39, 46], [25, 57]], [[10, 18], [50, 70]], [[8, 17], [28, 55]], [[76, 11], [36, 47]], [[4, 16], [35, 64]], [[75, 13], [26, 56]], [[34, 49], [42, 67]], [[74, 15], [27, 61]], [[72, 14], [23, 58]], [[52, 71], [30, 54]], [[48, 69], [31, 53]], [[40, 66], [24, 60]], [[37, 65], [29, 62]]]
57 --> [[[1, 20], [32, 50]], [[21, 58], [31, 62]], [[18, 19], [40, 42]], [[2, 5], [4, 8]], [[76, 6], [72, 11]], [[37, 43], [44, 67]], [[38, 45], [24, 56]], [[9, 17], [49, 69]], [[7, 16], [27, 54]], [[75, 10], [35, 46]], [[3, 15], [34, 63]], [[74, 12], [25, 55]], [[33, 48], [41, 66]], [[73, 14], [26, 60]], [[71, 13], [22, 57]], [[51, 70], [29, 53]], [[47, 68], [30, 52]], [[39, 65], [23, 59]], [[36, 64], [28, 61]]]
58 --> [[[1, 19], [31, 49]], [[20, 57], [30, 61]], [[17, 18], [39, 41]], [[76, 4], [3, 7]], [[75, 5], [71, 10]], [[36, 42], [43, 66]], [[37, 44], [23, 55]], [[8, 16], [48, 68]], [[6, 15], [26, 53]], [[74, 9], [34, 45]], [[2, 14], [33, 62]], [[73, 11], [24, 54]], [[32, 47], [40, 65]], [[72, 13], [25, 59]],
[[70, 12], [21, 56]], [[50, 69], [28, 52]], [[46, 67], [29, 51]], [[38, 64], [22, 58]], [[35, 63], [27, 60]]]
59 --> [[[1, 18], [30, 48]], [[19, 56], [29, 60]], [[16, 17], [38, 40]], [[75, 3], [2, 6]], [[74, 4], [70, 9]], [[35, 41], [42, 65]], [[36, 43], [22, 54]], [[7, 15], [47, 67]], [[5, 14], [25, 52]], [[73, 8], [33, 44]], [[76, 13], [32, 61]], [[72, 10], [23, 53]], [[31, 46], [39, 64]], [[71, 12], [24, 58]], [[69, 11], [20, 55]], [[49, 68], [27, 51]], [[45, 66], [28, 50]], [[37, 63], [21, 57]], [[34, 62], [26, 59]]]
60 --> [[[1, 17], [29, 47]], [[18, 55], [28, 59]], [[15, 16], [37, 39]], [[74, 2], [76, 5]], [[73, 3], [69, 8]], [[34, 40], [41, 64]], [[35, 42], [21, 53]], [[6, 14], [46, 66]], [[4, 13], [24, 51]], [[72, 7], [32, 43]], [[75, 12], [31, 60]], [[71, 9], [22, 52]], [[30, 45], [38, 63]], [[70, 11], [23, 57]], [[68, 10], [19, 54]], [[48, 67], [26, 50]], [[44, 65], [27, 49]], [[36, 62], [20, 56]], [[33, 61], [25, 58]]]
61 --> [[[1, 16], [28, 46]], [[17, 54], [27, 58]], [[14, 15], [36, 38]], [[73, 76], [75, 4]], [[72, 2], [68, 7]], [[33, 39], [40, 63]], [[34, 41], [20, 52]], [[5, 13], [45, 65]], [[3, 12], [23, 50]], [[71, 6], [31, 42]], [[74, 11], [30, 59]], [[70, 8], [21, 51]], [[29, 44], [37, 62]], [[69, 10], [22, 56]], [[67, 9], [18, 53]], [[47, 66], [25, 49]], [[43, 64], [26, 48]], [[35, 61], [19, 55]], [[32, 60], [24, 57]]]
62 --> [[[1, 15], [27, 45]], [[16, 53], [26, 57]], [[13, 14], [35, 37]], [[72, 75], [74, 3]], [[71, 76], [67, 6]], [[32, 38], [39, 62]], [[33, 40], [19, 51]], [[4, 12], [44, 64]], [[2, 11], [22, 49]], [[70, 5], [30, 41]], [[73, 10], [29, 58]], [[69, 7], [20, 50]], [[28, 43], [36, 61]], [[68, 9], [21, 55]], [[66, 8], [17, 52]], [[46, 65], [24, 48]], [[42, 63], [25, 47]], [[34, 60], [18, 54]], [[31, 59], [23, 56]]]
63 --> [[[1, 14], [26, 44]], [[15, 52], [25, 56]], [[12, 13], [34, 36]], [[71, 74], [73, 2]], [[70, 75], [66, 5]], [[31, 37], [38, 61]], [[32, 39], [18, 50]], [[3, 11], [43, 63]], [[76, 10], [21, 48]], [[69, 4], [29, 40]], [[72, 9], [28, 57]], [[68, 6], [19, 49]], [[27, 42], [35, 60]], [[67, 8], [20, 54]], [[65, 7], [16, 51]], [[45, 64], [23, 47]], [[41, 62], [24, 46]], [[33, 59], [17, 53]], [[30, 58], [22, 55]]]
64 --> [[[1, 13], [25, 43]], [[14, 51], [24, 55]], [[11, 12], [33, 35]], [[70, 73], [72, 76]], [[69, 74], [65, 4]], [[30, 36], [37, 60]], [[31, 38], [17, 49]], [[2, 10], [42, 62]], [[75, 9], [20, 47]], [[68, 3], [28, 39]], [[71, 8], [27, 56]], [[67, 5], [18, 48]], [[26, 41], [34, 59]], [[66, 7], [19, 53]], [[64, 6], [15, 50]], [[44, 63], [22, 46]], [[40, 61], [23, 45]], [[32, 58], [16, 52]], [[29, 57], [21, 54]]]
65 --> [[[1, 12], [24, 42]], [[13, 50], [23, 54]], [[10, 11], [32, 34]], [[69, 72], [71, 75]], [[68, 73], [64, 3]], [[29, 35], [36, 59]], [[30, 37], [16, 48]], [[76, 9], [41, 61]], [[74, 8], [19, 46]], [[67, 2], [27, 38]], [[70, 7], [26, 55]], [[66, 4], [17, 47]], [[25, 40], [33, 58]], [[65, 6], [18, 52]], [[63, 5], [14, 49]], [[43, 62], [21, 45]], [[39, 60], [22, 44]], [[31, 57], [15, 51]], [[28, 56], [20, 53]]]
66 --> [[[1, 11], [23, 41]], [[12, 49], [22, 53]], [[9, 10], [31, 33]], [[68, 71], [70, 74]], [[67, 72], [63, 2]], [[28, 34], [35, 58]], [[29, 36], [15, 47]], [[75, 8], [40, 60]], [[73, 7], [18, 45]], [[66, 76], [26, 37]], [[69, 6], [25, 54]], [[65, 3], [16, 46]], [[24, 39], [32, 57]], [[64, 5], [17, 51]], [[62, 4], [13, 48]], [[42, 61], [20, 44]], [[38, 59], [21, 43]], [[30, 56], [14, 50]], [[27, 55], [19, 52]]]
67 --> [[[1, 10], [22, 40]], [[11, 48], [21, 52]], [[8, 9], [30, 32]], [[67, 70], [69, 73]], [[66, 71],
[62, 76]], [[27, 33], [34, 57]], [[28, 35], [14, 46]], [[74, 7], [39, 59]], [[72, 6], [17, 44]], [[65, 75], [25, 36]], [[68, 5], [24, 53]], [[64, 2], [15, 45]], [[23, 38], [31, 56]], [[63, 4], [16, 50]], [[61, 3], [12, 47]], [[41, 60], [19, 43]], [[37, 58], [20, 42]], [[29, 55], [13, 49]], [[26, 54], [18, 51]]]
68 --> [[[1, 9], [21, 39]], [[10, 47], [20, 51]], [[7, 8], [29, 31]], [[66, 69], [68, 72]], [[65, 70], [61, 75]], [[26, 32], [33, 56]], [[27, 34], [13, 45]], [[73, 6], [38, 58]], [[71, 5], [16, 43]], [[64, 74], [24, 35]], [[67, 4], [23, 52]], [[63, 76], [14, 44]], [[22, 37], [30, 55]], [[62, 3], [15, 49]], [[60, 2], [11, 46]], [[40, 59], [18, 42]], [[36, 57], [19, 41]], [[28, 54], [12, 48]], [[25, 53], [17, 50]]]
69 --> [[[1, 8], [20, 38]], [[9, 46], [19, 50]], [[6, 7], [28, 30]], [[65, 68], [67, 71]], [[64, 69], [60, 74]], [[25, 31], [32, 55]], [[26, 33], [12, 44]], [[72, 5], [37, 57]], [[70, 4], [15, 42]], [[63, 73], [23, 34]], [[66, 3], [22, 51]], [[62, 75], [13, 43]], [[21, 36], [29, 54]], [[61, 2], [14, 48]], [[59, 76], [10, 45]], [[39, 58], [17, 41]], [[35, 56], [18, 40]], [[27, 53], [11, 47]], [[24, 52], [16, 49]]]
70 --> [[[1, 7], [19, 37]], [[8, 45], [18, 49]], [[5, 6], [27, 29]], [[64, 67], [66, 70]], [[63, 68], [59, 73]], [[24, 30], [31, 54]], [[25, 32], [11, 43]], [[71, 4], [36, 56]], [[69, 3], [14, 41]], [[62, 72], [22, 33]], [[65, 2], [21, 50]], [[61, 74], [12, 42]], [[20, 35], [28, 53]], [[60, 76], [13, 47]], [[58, 75], [9, 44]], [[38, 57], [16, 40]], [[34, 55], [17, 39]], [[26, 52], [10, 46]], [[23, 51], [15, 48]]]
71 --> [[[1, 6], [18, 36]], [[7, 44], [17, 48]], [[4, 5], [26, 28]], [[63, 66], [65, 69]], [[62, 67], [58, 72]], [[23, 29], [30, 53]], [[24, 31], [10, 42]], [[70, 3], [35, 55]], [[68, 2], [13, 40]], [[61, 71], [21, 32]], [[64, 76], [20, 49]], [[60, 73], [11, 41]], [[19, 34], [27, 52]], [[59, 75], [12, 46]], [[57, 74], [8, 43]], [[37, 56], [15, 39]], [[33, 54], [16, 38]], [[25, 51], [9, 45]], [[22, 50], [14, 47]]]
72 --> [[[1, 5], [17, 35]], [[6, 43], [16, 47]], [[3, 4], [25, 27]], [[62, 65], [64, 68]], [[61, 66], [57, 71]], [[22, 28], [29, 52]], [[23, 30], [9, 41]], [[69, 2], [34, 54]], [[67, 76], [12, 39]], [[60, 70], [20, 31]], [[63, 75], [19, 48]], [[59, 72], [10, 40]], [[18, 33], [26, 51]], [[58, 74], [11, 45]], [[56, 73], [7, 42]], [[36, 55], [14, 38]], [[32, 53], [15, 37]], [[24, 50], [8, 44]], [[21, 49], [13, 46]]]
73 --> [[[1, 4], [16, 34]], [[5, 42], [15, 46]], [[2, 3], [24, 26]], [[61, 64], [63, 67]], [[60, 65], [56, 70]], [[21, 27], [28, 51]], [[22, 29], [8, 40]], [[68, 76], [33, 53]], [[66, 75], [11, 38]], [[59, 69], [19, 30]], [[62, 74], [18, 47]], [[58, 71], [9, 39]], [[17, 32], [25, 50]], [[57, 73], [10, 44]], [[55, 72], [6, 41]], [[35, 54], [13, 37]], [[31, 52], [14, 36]], [[23, 49], [7, 43]], [[20, 48], [12, 45]]]
74 --> [[[1, 3], [15, 33]], [[4, 41], [14, 45]], [[76, 2], [23, 25]], [[60, 63], [62, 66]], [[59, 64], [55, 69]], [[20, 26], [27, 50]], [[21, 28], [7, 39]], [[67, 75], [32, 52]], [[65, 74], [10, 37]], [[58, 68], [18, 29]], [[61, 73], [17, 46]], [[57, 70], [8, 38]], [[16, 31], [24, 49]], [[56, 72], [9, 43]], [[54, 71], [5, 40]], [[34, 53], [12, 36]], [[30, 51], [13, 35]], [[22, 48], [6, 42]], [[19, 47], [11, 44]]]
75 --> [[[1, 2], [14, 32]], [[3, 40], [13, 44]], [[75, 76], [22, 24]], [[59, 62], [61, 65]], [[58, 63], [54, 68]], [[19, 25], [26, 49]], [[20, 27], [6, 38]], [[66, 74], [31, 51]], [[64, 73], [9, 36]], [[57, 67], [17, 28]], [[60, 72], [16, 45]], [[56, 69], [7, 37]], [[15, 30], [23, 48]], [[55, 71], [8, 42]],
[[53, 70], [4, 39]], [[33, 52], [11, 35]], [[29, 50], [12, 34]], [[21, 47], [5, 41]], [[18, 46], [10, 43]]]
