--description--

$2^N$ binary digits can be placed in a circle so that all the $N$-digit clockwise subsequences are distinct.

For $N = 3$, two such circular arrangements are possible, ignoring rotations:

For the first arrangement, the 3-digit subsequences, in clockwise order, are: 000, 001, 010, 101, 011, 111, 110 and 100.

Each circular arrangement can be encoded as a number by concatenating the binary digits starting with the subsequence of all zeros as the most significant bits and proceeding clockwise. The two arrangements for $N = 3$ are thus represented as 23 and 29:

$${00010111}_2 = 23\\ {00011101}_2 = 29$$

Calling $S(N)$ the sum of the unique numeric representations, we can see that $S(3) = 23 + 29 = 52$.

Find $S(5)$.

--hints--

binaryCircles() should return 209110240768.

assert.strictEqual(binaryCircles(), 209110240768);

--seed--

--seed-contents--

function binaryCircles() {

  return true;
}

binaryCircles();

--solutions--

// solution required