--description--

A positive integer will be called reachable if it can result from an arithmetic expression obeying the following rules:

• Uses the digits 1 through 9, in that order and exactly once each.
• Any successive digits can be concatenated (for example, using the digits 2, 3 and 4 we obtain the number 234).
• Only the four usual binary arithmetic operations (addition, subtraction, multiplication and division) are allowed.
• Each operation can be used any number of times, or not at all.
• Unary minus is not allowed.
• Any number of (possibly nested) parentheses may be used to define the order of operations.

For example, 42 is reachable, since $\frac{1}{23} \times ((4 \times 5) - 6) \times (78 - 9) = 42$.

What is the sum of all positive reachable integers?

--hints--

reachableNumbers() should return 20101196798.

assert.strictEqual(reachableNumbers(), 20101196798);

--seed--

--seed-contents--

function reachableNumbers() {

  return true;
}

reachableNumbers();

--solutions--

// solution required