--description--

Consider the alphabet $A$ made out of the letters of the word project: $A = \{c, e, j, o, p, r, t\}$.

Let $T(n)$ be the number of strings of length $n$ consisting of letters from $A$ that do not have a substring that is one of the 5040 permutations of project.

$T(7) = 7^7 - 7! = 818\,503$.

Find $T({10}^{12})$. Give the last 9 digits of your answer.

--hints--

permutationsOfProject() should return 423341841.

assert.strictEqual(permutationsOfProject(), 423341841);

--seed--

--seed-contents--

function permutationsOfProject() {

  return true;
}

permutationsOfProject();

--solutions--

// solution required