from collections import defaultdict,deque,Counter
def run(load,read,check):
 r=load('C286_DATA.json')['target_register'];ix=defaultdict(list)
 for i,z in enumerate(r):ix[z['center']].append(i)
 X=sorted(ix);C=[3188,3190,3248,3250];adj={x:[] for x in X};edges=[]
 for x in X:
  for c in C:
   y=2*c-x
   if y in ix:
    adj[x].append((y,c))
    if x<=y:edges.append({'lower':x,'upper':y,'center':c,'lower_indices':ix[x],'upper_indices':ix[y]})
 remaining=set(X);comps=[];witnesses=[]
 while remaining:
  start=min(remaining);seen={start};q=deque([start])
  while q:
   x=q.popleft()
   for y,c in adj[x]:
    if y not in seen:seen.add(y);q.append(y)
  remaining-=seen;comp=sorted(seen);diam=0
  for start in comp:
   paths={start:[]};q=deque([start])
   while q:
    x=q.popleft()
    for y,c in adj[x]:
     if y not in paths:paths[y]=paths[x]+[{'from':x,'center':c,'to':y}];q.append(y)
   check(f'connected_{start}',set(paths)==seen)
   for end in comp:
    if start<end:
     p=paths[end];diam=max(diam,len(p));witnesses.append({'input':start,'output':end,'gap':end-start,'length':len(p),'path':p})
  ee=[e for e in edges if e['lower'] in seen]
  comps.append({'coordinates':comp,'size':len(comp),'edges':len(ee),'loops':sum(e['lower']==e['upper'] for e in ee),'diameter':diam,'span':comp[-1]-comp[0]})
 check('edge census',len(edges)==106)
 return {'step':'C446','edges':edges,'components':comps,'shortest_witnesses':witnesses,'counts':{'coordinates':len(X),'edges_including_loops':len(edges),'components':len(comps),'nontrivial_components':sum(c['size']>1 for c in comps),'active_coordinates':sum(c['size'] for c in comps if c['edges']),'isolated_coordinates':sum(c['edges']==0 for c in comps),'component_size_distribution':dict(sorted(Counter(c['size'] for c in comps).items())),'max_diameter':max(c['diameter'] for c in comps),'reachable_distinct_pairs':len(witnesses)}}