from itertools import product

def run(load,check):
 rows=[];patterns={}
 for b in load('C279_DATA.json')['triangles']:
  for s,f,r in product(range(2),repeat=3):
   S=b['Shem_signed']-460*s;F=b['Flood_partner_signed']-460*f;R=b['regular_reflected']-460*r
   legs=[F-S,R-F,R-S];form=[598+460*(s-f),8395+460*(f-r),8993+460*(s-r)]
   check(f'formula j{b["index_j"]} states{s}{f}{r}',legs==form and legs[0]+legs[1]==legs[2])
   check(f'23 divisibility j{b["index_j"]} states{s}{f}{r}',all(x%23==0 for x in legs))
   allK=all(x%529==0 for x in legs)
   row={'j':b['index_j'],'Shem_Cainan':s,'Flood_Cainan':f,'regular_profile':r,'widths':legs,'in23_units':[x//23 for x in legs],'all_K':allK}
   rows.append(row);patterns[(s,f,r)]=row
 hits=[x for x in rows if x['all_K']]
 check('unique allK profile',len(hits)==6 and {(x['Shem_Cainan'],x['Flood_Cainan'],x['regular_profile']) for x in hits}=={(1,0,1)})
 check('four17K patterns',sum(x['widths'][2]==8993 for x in patterns.values())==4)
 return {'all48_rows':rows,'eight_patterns':[dict(v,j='any2-7') for k,v in sorted(patterns.items())],'all_K_count':len(hits),'regular_profile_labels':{'0':'SP OFF full430 Terah0','1':'MT ON full430 Terah60'},'normalized_formula':['26+20(s-f)','365+20(f-r)','391+20(s-r)']}