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They call the U.S. men’s basketball team the “Dream Team,” but if anything the women’s team is even more dominant – in fact, for the other nations participating at the Rio Olympics, both squads are positively nightmarish.

The U.S. men’s team is hoping to win its third consecutive gold after a disappointing 2004 Olympics in which they lost to Argentina in the semifinals and had to settle for bronze.

The women, on the other hand, are going for their sixth straight Olympic gold medal, and a few of the team members, guards Diana Taurasi and Sue Bird and forward Tamika Catchings, have been together since 2004.

“This could be the last time we’re on the court together,” Taurasi told Fox News Latino after a recent practice session in Tarrytown, New York. “I don’t even want to think about it.”

Women’s coach Geno Auriemma pointed out that many of his squad members play for a WNBA team as well as a European one.

“With all those commitments,” Auriemma told reporters before the team left for Brazil, “this is their home base – coming together and playing with all these great players.”

Both the men and women’s teams have crisscrossed the U.S. in the run-up to the Olympics, delivering basketball blowouts from coast to coast before gathering Tuesday night in Houston to head for Brazil.

"This is the exciting part, knowing that we're about to go to Rio," men's star Carmelo Anthony said. "We're about to just lock in in just one location, and we can just really focus on playing basketball and getting better individually and as a group."

Anthony – the grizzled veteran of the team, who at 18 was a bench player on that disappointing 2004 team – wasn't a fan of the early morning flights that the Americans took during their exhibition tour, as evidenced by DeMar DeRozan's Instagram video of a team singalong during one trip.

Now the teams can drop anchor and stick around in one spot — they're staying on a cruise ship along one of Brazil's beautiful beaches.

"I'm excited to see (Kevin Durant), DeMarcus Cousins, all the guys. I like them all, and it's a great group of guys," Angel McCoughtry of the women's team said following its final exhibition in New York. "I'm ready to get to know them better and continue to hang out with these girls and have a good time in Rio. This is the Olympics, it's a positive thing and we're ready to go in there and have some fun."

The men finished off their exhibition tour here Monday with a 110-66 rout of Nigeria, a game attended by the women's team after it arrived earlier in the day. After unveiling their team in New York in late June, the men reported three weeks later to training camp in Las Vegas and also played exhibition games in Los Angeles, Oakland and Chicago.

They went 5-0, averaged 102.8 points and overwhelmed their opponents by 43 per game. The road to Rio was easy, but coach Mike Krzyzewski insists the Olympics won't be.

"The competition is going to get better. I mean, really good," Krzyzewski said.

"We play two games against teams that we've beaten, but they'll be a little bit different, in China and Venezuela. And then we play Australia, who is very good. They'll probably start five NBA players. And then you play Serbia, and we know them from the world championships, with (Milos) Teodosic and their big guys. And then you play France, who will probably have eight or nine NBA players. So it goes up. It goes up, and we have to react accordingly."

The U.S. crushed China, the opponent in its opener Saturday, 106-57 and 107-57. The Americans beat Venezuela 80-45.

The women played higher-caliber opponents during their tour, which started in Los Angeles before moving to the Northeast for victories over France, Canada and Australia. They have won 41 consecutive Olympic contests, with the last loss coming in the 1992 semifinals.

Auriemma noted that the women haven’t had much time to gel, with its first real practice happening on July 23. He said Tuesday that he plans another Wednesday after they arrive in Rio.

"So we're not as good as we're going to be, and that's kind of the way it's been for us at the Olympics," Auriemma said. "We get better as the week goes on, and that's certainly been the case since the 23rd."

But last weekend Auriemma, who was at the helm of the 2012 team that defeated France by 36 points in the gold medal match, said something that should give Team USA’s opponents grave misgivings: “In some ways I think this can be the best U.S. team ever.”

He went on, “The combination of talent and experience, the versatility of this team – this may be the best. But now they have to prove it.”

Durant and Anthony are the only players on the men's team who have played in the Olympics before, but there was still plenty of learning to do on and off the court during the tour – even for the women – with more still come when the games start to count.

"I think there's a level of comfort now that you can tell that we have from our first game to our last warmup game," Maya Moore said.

The Associated Press contributed to this report.

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