--description--

A $k$-input binary truth table is a map from $k$ input bits (binary digits, 0 [false] or 1 [true]) to 1 output bit. For example, the $2$-input binary truth tables for the logical $AND$ and $XOR$ functions are:

How many $6$-input binary truth tables, $τ$, satisfy the formula

$$τ(a, b, c, d, e, f) \; AND \; τ(b, c, d, e, f, a \; XOR \; (b \; AND \; c)) = 0$$

for all $6$-bit inputs ($a$, $b$, $c$, $d$, $e$, $f$)?

--hints--

circularLogic() should return 15964587728784.

assert.strictEqual(circularLogic(), 15964587728784);

--seed--

--seed-contents--

function circularLogic() {

  return true;
}

circularLogic();

--solutions--

// solution required