--description--

There are 1111 ways in which five 6-sided dice (sides numbered 1 to 6) can be rolled so that the top three sum to 15. Some examples are:

$$\begin{align} & D_1,D_2,D_3,D_4,D_5 = 4,3,6,3,5 \\ & D_1,D_2,D_3,D_4,D_5 = 4,3,3,5,6 \\ & D_1,D_2,D_3,D_4,D_5 = 3,3,3,6,6 \\ & D_1,D_2,D_3,D_4,D_5 = 6,6,3,3,3 \end{align}$$

In how many ways can twenty 12-sided dice (sides numbered 1 to 12) be rolled so that the top ten sum to 70?

--hints--

topDice() should return 7448717393364182000.

assert.strictEqual(topDice(), 7448717393364182000);

--seed--

--seed-contents--

function topDice() {

  return true;
}

topDice();

--solutions--

// solution required