E651. Les distributions de chocolats ****
A la récréation, le maître d'école invite le petit Nicolas et ses camarades ‒ sauf Eudes qui est toujours en retard ‒ à former un grand cercle et il leur annonce la distribution d'un paquet de chocolats selon les règles suivantes : il donne un chocolat au petit Nicolas puis en se déplaçant dans le sens des aiguilles d'une montre, il saute un enfant et donne un chocolat au suivant, puis il saute deux enfants et donne un chocolat au suivant, puis il saute trois enfants et donne un chocolat au suivant... Après avoir effectué plusieurs tours de cercle, le maître donne le dernier chocolat au petit Nicolas qui au total en a reçu quatre comme certains de ses camarades. D'autres enfants en ont reçu deux et tous les autres n'ont rien reçu.
Eudes arrive enfin et s'intercale entre deux de ses camarades le long du grand cercle. Avec un deuxième paquet de chocolats de même contenance que le premier, le maître effectue une nouvelle distribution selon les mêmes règles en partant cette fois-ci d'Eudes qui reçoit le premier chocolat. Lorsque le paquet est vide, tous les enfants sauf un ont reçu soit un chocolat soit deux chocolats.
Determiner le nombre d'enfants dans la classe du petit Nicolas et le nombre de chocolats contenus dans chaque paquet
Si n personnes composent la classe, alors la boîte contient au maximum 2 n1 chocolats et au minimum n chocolats (voir la distribution avec Eudes)
Un automate permet de résoudre le problème Deux solutions :
8 enfants (avec Nicolas) dans la classe et 12 chocolats par paquet ou
32 enfants (avec Nicolas) dans la classe et 60 chocolats par paquets
Vérifications « manuelle », détails du déroulement de la distribution des chocolats : Solution 1 :
Sans Eudes [1, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0]
[1, 0, 2, 0, 0, 1, 0]
[2, 0, 2, 0, 0, 1, 0]
[2, 0, 2, 0, 0, 1, 1]
[2, 0, 2, 0, 0, 1, 2]
[3, 0, 2, 0, 0, 1, 2]
[3, 0, 3, 0, 0, 1, 2]
[3, 0, 3, 0, 0, 2, 2]
[3, 0, 4, 0, 0, 2, 2]
[4, 0, 4, 0, 0, 2, 2]
Nicolas est en première position et reçoit le premier et le dernier chocolat
Avec Eudes
[1, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 1, 1, 0]
[1, 1, 1, 0, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 2, 1, 1, 1, 0]
[1, 1, 1, 2, 2, 1, 1, 0]
[1, 1, 1, 2, 2, 1, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 0]
[1, 2, 1, 2, 2, 2, 2, 0]
Tous les enfants sauf un reçoivent 1 ou 2 chocolats
S
olution 2 :
Sans Eudes
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 0, 0]
[1, 0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[1, 0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[1, 0, 1, 2, 2, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[1, 0, 1, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[1, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0]
[2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1]
[2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 3, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 3, 0, 0, 0, 3, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 3, 0, 0, 0, 3, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 3, 0, 0, 0, 3, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2]
[3, 0, 3, 2, 2, 3, 0, 0, 0, 3, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 2, 3, 3, 0, 0, 0, 3, 0, 2, 0, 2, 3, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 2, 3, 3, 0, 0, 0, 3, 0, 2, 0, 3, 3, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 2, 3, 3, 0, 0, 0, 3, 0, 2, 0, 3, 3, 2, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 2, 0, 3, 3, 2, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 2, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 1, 3, 2, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 2, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 1, 3, 3, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 1, 3, 3, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 3, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 2, 3, 3, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 4, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 2, 3, 3, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 4, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 3, 3, 3, 0, 0, 0, 3, 0, 4, 0, 3, 3, 4, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 4, 3, 3, 0, 0, 0, 3, 0, 4, 0, 3, 3, 4, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 4, 3, 3, 0, 0, 0, 3, 0, 4, 0, 3, 3, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 4, 3, 3, 0, 0, 0, 3, 0, 4, 0, 4, 3, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 4, 4, 3, 0, 0, 0, 3, 0, 4, 0, 4, 3, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 2, 3, 4, 0, 2]
[3, 0, 3, 4, 4, 3, 0, 0, 0, 3, 0, 4, 0, 4, 3, 4, 0, 0, 0, 0, 3, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[3, 0, 3, 4, 4, 3, 0, 0, 0, 3, 0, 4, 0, 4, 3, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[3, 0, 3, 4, 4, 3, 0, 0, 0, 3, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[3, 0, 3, 4, 4, 3, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[3, 0, 3, 4, 4, 4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[3, 0, 4, 4, 4, 4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
[4, 0, 4, 4, 4, 4, 0, 0, 0, 4, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 4, 4, 0, 2]
Nicolas est en première position et reçoit le premier et le dernier chocolat
Avec Eudes
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
[1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0]
[1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]
[1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]
[1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0]
[1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0]
