MOD = 10**7
SPACE = 10**7
CACHE = [None for _ in range(SPACE * 2)]
CACHE_TILL = [None for _ in range(SPACE)]
CACHE_TILL_IS_TWO_EVEN = [None for _ in range(SPACE)]
CACHE_TILL_IS_TWO_ODD = [None for _ in range(SPACE)]
CACHE_T_FROM_ACC = [None for _ in range(SPACE * 2)]


def t_from_acc(rem: int, is_two: bool) -> int:
    offset = rem + SPACE * is_two
    if (value := CACHE_T_FROM_ACC[offset]) is not None:
        return value
    if rem < 0:
        return 0
    s = t_from(rem, is_two) + t_from_acc(rem - 2, is_two)
    s %= MOD
    CACHE_T_FROM_ACC[offset] = s
    return s


def t_from(rem: int, is_two: bool) -> int:
    offset = rem + SPACE * is_two
    if (value := CACHE[offset]) is not None:
        return value
    s = 0
    if rem < 0:
        s = 0
    elif rem == 1:
        s = 0
    elif rem == 0 and is_two:
        s = 1
    else:
        s += t_from(rem - 2, is_two)  # d = 1
        s %= MOD
        s += t_from(rem - 4, True)  # d = 2
        s %= MOD
        s += t_from_acc(rem - 6, is_two)
        s %= MOD
        # Naive (too slow):
        # for d in range(1, rem // 2 + 1):
        #     s += t_from(rem - 2 * d, is_two or d == 2)
        #     s %= MOD
    CACHE[offset] = s % MOD
    return s % MOD


def t_old(n: int) -> int:
    # print(f"t({n}) = ", end="")
    s = 0
    for i in range(0, n + 1):
        rem = n - i
        s += t_from(rem, i == 2)
    return s % MOD


def t(n: int) -> int:
    s = CACHE_TILL[n - 4]
    assert s is not None
    s += t_from(n - 3, False)
    CACHE_TILL[n - 3] = s % MOD
    s += t_from(n - 2, True)
    s %= MOD
    s += t_from(n - 1, False)
    s %= MOD
    s += t_from(n, False)
    s %= MOD
    return s


def euler_710():
    for i in range(4):
        CACHE_TILL[i] = 0

    for n in range(4, 50):
        t(n)
    assert t(5) == 1
    assert t(6) == 4
    assert t(20) == 824
    assert t(42) == 1999923

    for n in range(10, SPACE):
        tn = t(n)
        if tn % 10**6 == 0:
            # print(f"t({n}) = {tn} <<<")
            return n
        # if tn % 10000 == 0:
        #     print(f"t({n}) = {tn}")
    assert False, "Solution not found"


if __name__ == "__main__":
    solution = euler_710()
    print(f"e710.py: {solution}")
    assert solution == 1275000