from collections import Counter
from itertools import product

def run(load,read,check):
    reg=load('C286_DATA.json')['target_register'];allpairs=load('C438_DATA.json')['labelled_pairs']
    A=[z for z in allpairs if z['roles']==['Noah birth','Shem death']]
    B=[z for z in allpairs if z['roles'] in [['Flood start','Shem birth'],['Flood close','Shem birth']]]
    def key(row):return (row['center'],row['lower_record'],row['upper_record'])
    def target(source,role,rail):
        return [i for i,r in enumerate(reg) if r['role']==role and r.get('rail')==rail and all(r[k]==source[k] for k in ['tradition','gear','Cainan','Terah60','full430'])]
    mapped=[]
    for z in A:
        nd={reg[z[k]]['role']:z[k] for k in ['lower_record','upper_record']};n,s=reg[nd['Noah birth']],reg[nd['Shem death']]
        sb=target(n,'Shem birth',n.get('rail'));fl=target(s,'Flood close' if s.get('rail')=='companion' else 'Flood start',None)
        check('unique source-preserving transport '+str(key(z)),len(sb)==len(fl)==1)
        i,j=sb[0],fl[0]
        check('opposed500 preserves sum '+str(key(z)),reg[i]['center']==n['center']-500 and reg[j]['center']==s['center']+500 and reg[i]['center']+reg[j]['center']==2*z['center'])
        a,b=sorted([i,j],key=lambda k:reg[k]['center'])
        mapped.append({'source':z,'Shem_birth_record':i,'Flood_record':j,'target_key':[z['center'],a,b],'ordering_reversed':reg[i]['center']<reg[j]['center']})
    image={tuple(z['target_key']) for z in mapped};targetset={key(z) for z in B}
    sourcecoords={(z['center'],z['lower'],z['upper']) for z in A}
    imagecoords={(c,reg[i]['center'],reg[j]['center']) for c,i,j in image};targetcoords={(z['center'],z['lower'],z['upper']) for z in B}
    check('coordinate bijection has16 source and16 target pairs',len(sourcecoords)==len(imagecoords)==len(targetcoords)==16 and imagecoords==targetcoords)
    check('typed image is injective40 of48 labels',len(mapped)==len(image)==40 and len(targetset)==48 and image<=targetset)
    extras=sorted(targetset-image)
    check('eight additional LXX Flood-close aliases only',len(extras)==8 and all(any(reg[i]['tradition']=='LXX' and reg[i]['role']=='Flood close' for i in [a,b]) and any(reg[i]['tradition']=='SP' and reg[i]['role']=='Shem birth' and reg[i].get('rail')=='companion' for i in [a,b]) for _,a,b in extras))
    reversed_rows=[z for z in mapped if z['ordering_reversed']]
    check('one coordinate-order reversal',len(reversed_rows)==1 and reversed_rows[0]['source']['center']==3250 and [reg[reversed_rows[0][k]]['center'] for k in ['Shem_birth_record','Flood_record']]==[3205,3295])
    templates=Counter()
    for z in A:
        a,b=[reg[z[k]] for k in ['lower_record','upper_record']]
        v=(z['center'],a['Cainan']+b['Cainan'],a['Terah60']+b['Terah60'],a['full430']+b['full430'],a['gear']+b['gear'],int(a.get('rail')=='companion')+int(b.get('rail')=='companion'))
        templates[v]+=1
    expected={(3188,0,1,2,4,0):24,(3188,0,1,2,5,2):4,(3190,0,1,2,6,0):8,(3250,1,1,2,2,2):4}
    check('four source sum templates',dict(templates)==expected)
    abstract=[]
    for c in [3188,3190,3248,3250]:
        for cs,ts,fs,gs,es in product(range(3),range(3),range(3),range(2,7),range(3)):
            if 5882+130*cs+60*ts+215*fs+2*(gs-2)-es==2*c:abstract.append((c,cs,ts,fs,gs,es))
    check('bounded source-sum equation is complete',set(abstract)==set(expected))
    return {'step':'C440','source_pairs':A,'target_pairs':B,'record_preserving_transports':mapped,'additional_aliases':[{'center':c,'lower_record':a,'upper_record':b,'lower':reg[a],'upper':reg[b]} for c,a,b in extras],
            'source_sum_templates':[{'center':k[0],'Csum':k[1],'Tsum':k[2],'Fsum':k[3],'Gsum':k[4],'companion_sum':k[5],'labels':v} for k,v in sorted(templates.items())],
            'counts':{'coordinate_source_pairs':16,'coordinate_target_pairs':16,'source_label_pairs':40,'typed_image_label_pairs':40,'target_label_pairs':48,'additional_LXX_Flood_close_aliases':8,'ordering_reversals':1},
            'scope':'Opposed500 changes two different endpoints, preserving their sum; it is not a common translation of one chronology. A Flood-close alias is not an LXX companion rail.'}