import hashlib
import secrets


def hash_password(password: str, iterations: int = 200_000) -> str:
    salt = secrets.token_bytes(16)
    digest = hashlib.pbkdf2_hmac("sha256", password.encode("utf-8"), salt, iterations)
    return f"pbkdf2_sha256${iterations}${salt.hex()}${digest.hex()}"


def verify_password(password: str, password_hash: str) -> bool:
    try:
        algorithm, rounds_raw, salt_hex, digest_hex = password_hash.split("$", 3)
        if algorithm != "pbkdf2_sha256":
            return False
        rounds = int(rounds_raw)
        salt = bytes.fromhex(salt_hex)
        expected = bytes.fromhex(digest_hex)
    except (ValueError, TypeError):
        return False

    candidate = hashlib.pbkdf2_hmac("sha256", password.encode("utf-8"), salt, rounds)
    return secrets.compare_digest(candidate, expected)