"""Exact arithmetic model of Day 22/24 choices; no visitor data."""
from fractions import Fraction as F
import json

def recover(start, length):
    a, w, path = F(0), F(1), ''
    while (a, w) != (start, length):
        cut = a + w/3
        if start + length <= cut:
            path += 'L'; w /= 3
        elif start >= cut:
            path += 'R'; a = cut; w *= F(2,3)
        else:
            raise ValueError('Target crosses a division')
        if len(path)>11: raise ValueError('Unreachable interval')
    return path

rows=[]
def walk(a,w,path):
    decoded=recover(a,w)
    assert decoded==path
    terminal=w<F(1,64)
    rows.append({'path':path,'start':str(a),'length':str(w),'decoded':decoded,'terminal':terminal})
    if not terminal:
        walk(a,w/3,path+'L')
        walk(a+w/3,w*F(2,3),path+'R')
walk(F(0),F(1),'')
assert len({(r['start'],r['length']) for r in rows})==len(rows)
print(json.dumps({'method':'Exhaustive exact rational enumeration and recovery from final start and length; model only, no browser pixels or participant choices.','states':len(rows),'terminalStates':sum(r['terminal'] for r in rows),'maxChoices':max(len(r['path']) for r in rows),'allPathsRecovered':True,'rows':rows},indent=2))