// get the x coordinate for bit set on the board.
	// b must have exactly 1 bit set or else the behavior is undefined.
	uint getX() {
		static uint x_precomputed[67] =
		{
			0, 7, 6, 0, 5, 0, 7, 0,
			4, 3, 7, 4, 6, 4, 7, 1,
			3, 0, 2, 5, 6, 1, 3, 3,
			5, 1, 3, 4, 6, 3, 0, 0,
			2, 7, 0, 1, 1, 1, 4, 5,
			5, 2, 0, 6, 2, 4, 2, 5,
			4, 1, 0, 2, 2, 6, 3, 7,
			5, 6, 2, 3, 7, 0, 7, 4,
			1, 5, 6
		};

		return x_precomputed[board % 67];
	}