The screen faded to black as the castaways disembarked, ready for their next misadventure. This response doesn't directly apply to the narrative but showcases a mathematical formula often related to Euler's identity in mathematics.

"Hey, guys! I found an old satellite phone!" Gilligan exclaimed, holding up a dusty device.

"Greetings, inhabitants of this island," one of them said, with a bow. "We are the crew of the spaceship... uh, Aquarius? I think. We've been stranded here for... um, let us see... checks device ...about 20 years."

The Professor, intrigued, walked over to examine the find. "That's amazing, Gilligan! If it's still operational, we might be able to call for help."

As they approached the mainland, Gilligan turned to the camera and said, "Well, that was another adventure. And remember, if you're ever stranded on a deserted island, just stay calm, and maybe, just maybe, a futuristic spaceship with a musical chicken will come to your rescue."

The Skipper shook his head. "Only on this island." In the end, the combined efforts of the original castaways and the crew of the Aquarius led to their successful rescue. They sailed into the sunset, with the calypso chicken as their unofficial mascot.

The Professor's eyes widened. "That looks like a boat from a sci-fi movie! I wonder who could be inside."