RIO DE JANEIRO >> They teamed up for a carpool karaoke video. They planted their flag in Brazil. And when the Olympics are done, they’ll be remembered as the latest in a long line of U.S. swimming powerhouses.

So much for all those dire forecasts.

Turns out, the less-than-glittering times at the U.S. trials were no indication of how fast they would swim once they got to the big stage. And all those who thought they were too inexperienced to shine on the international stage totally missed the mark.

The Americans finished off the final night at the Olympic Aquatics Stadium by equaling their biggest medal haul in the last three decades.

Michael Phelps, Katie Ledecky & Co. made sure the U.S. stayed firmly atop the swimming world.

“We all know we’re part of a really special team,” Ledecky said Saturday, five medals hanging from her neck after one of the greatest performances in Olympic history. “We have such great depth in the U.S. in swimming, and it’s something we take great pride in. This is kind of our stage to show the world that.”

The Americans piled up 16 golds and 33 medals overall, matching their total from the 2000 Sydney Games.

Phelps, of course, led the way. In what he again insists will be his final Olympics, the 31-year-old piled up five golds and a silver, bouncing back from a stunning upset by Singapore’s Joseph Schooling in the 100-meter butterfly to help power the U.S. to victory in the final event at the pool, the 4×100 medley relay.

But no one was more dominant than the 19-year-old Ledecky, whose four golds included two world record-shattering performances. She joined Amy Van Dyken and Missy Franklin as the only American women to capture as many as four golds in a single games, matched Debbie Meyer as the only females to sweep the 200, 400 and 800 free, and also won silver anchoring the 4×100 free relay.

“What she’s doing in the sport is ridiculous,” Phelps said.

There’s something to be said for the camaraderie displayed by the American team.

During their final training session in Atlanta, a host of swimmers — Phelps and Ryan Lochte among them — took to the streets to record a James Corden-style carpool karaoke video . Even Ledecky took a turn behind the wheel, even though she still has just a learner’s permit.

“I was only at a gas station,” she quipped, “so I didn’t think I was going to hurt anyone.”

When the swimmers got to Brazil, they received a history lesson from one of the coaches, Greg Meehan. At a meeting with the female athletes on the eve of the games, he told them about the Homestead Act, the 1862 law that encouraged America’s westward migration by providing free land to settlers.

We’ll let Ledecky take it from there.

“We each had American flags and they printed out each of the events, and the people that were competing in each of those events came forward, had a little moment together, took the flag and stuck it through the paper and into the grass in the Olympic village,” she said. “We were just kind of staking our claim in Rio, and I think we kind of did that in the pool as well.”

In addition to Phelps and Ledecky, the biggest U.S. stars were Maya DiRado, who turned in the ultimate one-and-done with two golds and four medals overall; Ryan Murphy, who extended U.S. men’s dominance of the backstroke; Simone Manuel, the first African-American woman to win a gold medal with her victory in the 100 free, plus another gold in the women’s 4×100 medley relay; Lilly King, who backed up her brash diatribe against doping; and Anthony Ervin, the oldest member of the team at 35 and a gold medalist again in the 50 free — 16 years after he first won the event in Sydney.

Even with a hugely disappointing performance by Franklin, who didn’t even make it to the final of her two individual events, the Americans still blew everyone away.

There are several factors that go into the success of the U.S. program, starting with some simple numbers. The Americans have far more swimmers and resources to draw from than most nations, so it’s only natural they would dominate.

Beyond that, Ledecky pointed to a U.S. trials format that sets up the team to perform well at the Olympics. Over eight nights in Omaha, just a month before the games and following the same schedule of events, swimmers earned their way onto the team before sellout crowds of more than 14,000 at every session.

That was bigger than the crowds in Rio, where there were plenty of empty seats each night.

“It’s an overly easy environment for us to swim fast in because we’ve been through our Olympic trials, which is way more pressure-filled than the Olympics,” Ledecky said. “Obviously the crowd here hasn’t been that intimidating to us.”

Nothing was too intimidating to the Americans.

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Follow Paul Newberry on Twitter at www.twitter.com/pnewberry1963 . His work can be found at http://bigstory.ap.org/content/paul-newberry .