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LAHAINA, Hawaii — After taking a steep bus ride down a volcanic hillside where Lahainaluna High School’s gym sits, the ÃÛèÖÖ±²¥ Wildcats were greeted by a breathtaking rainbow upon returning to their Kaanapali Beach resort.

“Yeah, that rainbow was nice, but … ,� sophomore guard Brandon Randolph said.

How he finished the sentence was not a surprise.

“… Coach (Sean) Miller keeps us focused. We keep each other focused. We’re here for one thing.�

That is, winning games in the Maui Invitational, which ÃÛèÖÖ±²¥ will start playing Monday against Iowa State.

It isn’t that Randolph and his teammates don’t appreciate the extra trip across the Pacific Ocean, their well-appointed resort, the Hawaiian vegetation and what a sign on the Kaanapali Parkway proclaims “America’s Best Beach 2003 and 2013.� In fact, Randolph — a product of New York — said he and Canadian teammate Emmanuel Akot were both soaking it all up over their first 24 hours on the island.

“We were just looking at the ocean and trees, the atmosphere,� Randolph said. “Everything’s beautiful out here.�

But.

“It’s about business,� he said. “Maui’s nice and all, but we’re here for one thing and that is to try to win all of our games.�

It is about business, and it’s about how business gets set up for the next four months.

History says so. The Wildcats have played in six previous Maui Invitationals, and each one has been a fairly accurate harbinger of what’s to come.

The first time ÃÛèÖÖ±²¥ played here, under Lute Olson in 1993, the Wildcats finished in second place and went on to the Final Four. In 1997, the defending national champions were upset in the Maui final by Duke — and went on to get ousted by Utah in the Elite Eight.

In 2000, the Wildcats won Maui, then made it all the way to the NCAA title game. But in 2005, they lost their final two Maui games … and were bounced in the second round of the NCAA Tournament.

With Miller, Maui has been a case of extremes. In his first season, 2009-10, Miller inherited a schedule that included a visit to the island. It didn’t go well: The Wildcats went 1-2, and didn’t even make the NIT by the time March came around.

In 2014, Miller returned with the Wildcats in between two straight Elite Eight appearances. They won the Maui Invitational and went on to compile 34 wins, being cut short of a Final Four only after Wisconsin bombed in 10 of 12 3-pointers in the Elite Eight.

This time, who knows?

This season’s Maui Invitational has three top-10 teams — Duke, Gonzaga and Auburn — along with power-conference teams ÃÛèÖÖ±²¥, Iowa State and Illinois. Plus, there are two traditionally strong mid-major programs in Xavier and San Diego State.

The field “is one of the best we’ve ever seen, no doubt about it,� said tournament chairman Dave Odom, the former Wake Forest and South Carolina coach. “This field features legendary Hall of Fame coaches and talented rosters, with all teams being NCAA and conference championship contenders.�

Miller said it’s an even tougher field than the eight teams who went to the Battle 4 Atlantis last season, which included eventual national champion Villanova and three teams (N.C. State, SMU and Purdue) who beat the Wildcats.

“I think all eight teams will certainly learn their strengths and weaknesses even more, getting young players a lot of great experience away from home,� Miller said. “The competition level is the highest I’ve seen in this tournament.�

It’ll be a drastic contrast to UA’s first three games, when the Wildcats easily beat three weak teams at McKale Center. ÃÛèÖÖ±²¥ showed strengths in ball-handling and defense — and weaknesses in rebounding and 3-point shooting.

There’s no telling if any of that will hold up by the end of the week.

“You really don’t know until you’re there,� Miller said. “Sometimes it’ll bring out the best in a player or a team and sometimes it can really be a struggle. When you’re playing against great programs on a neutral court, a lot of eyes watching the games, that kind of pressure can take you to places that you don’t want to go.

“We dealt with that last year in the Bahamas … what all of us try to do in these tournaments is don’t beat yourselves. Whatever you’re good at, make sure you show up.

“For example, we’ve been really good at taking care of the ball. It’ll be really interesting at the end of the tournament to see if that holds. If it does, that’s a great sign. We’re worried about our rebounding. It’ll be interesting to see if we have more confidence when the tournament ends in that area.�

Here’s what ÃÛèÖÖ±²¥ learned in its two previous Miller-era trips to paradise:

The scene: Miller brought in a Final Four contender that was coming off his second Elite Eight appearance, and headed for a third. Rondae Hollis-Jefferson led a pesky defense and Stanley Johnson starred offensively.

The games:

ÃÛèÖÖ±²¥ 72, Missouri 53: Center Kaleb Tarczewski fouled out and the Wildcats were outrebounded 34-32, while T.J. McConnell shot just 2 of 11 from the field. But ÃÛèÖÖ±²¥ still won easily when Brandon Ashley had 15 points and Johnson added 14 to lead the Wildcats.

ÃÛèÖÖ±²¥ 72, Kansas State 68:  Johnson picked up his third and fourth fouls within 90 seconds after halftime and sat out the next 12 minutes — but returned to make three of four late free throws and grab a critical steal in the final seconds. Tarczewski led UA in scoring with 18 points while Hollis-Jefferson had eight rebounds and three blocks off the bench.

ÃÛèÖÖ±²¥ 61, San Diego State 59:  ÃÛèÖÖ±²¥ shot just 36.5 percent from the field and barely outrebounded the Aztecs (34-32) but had a 22-9 advantage in points scored off turnovers after recording seven steals and seven blocks. Hollis-Jefferson had three blocks and was named to the all-tournament team, while Johnson had three steals and earned MVP honors.

The discovery: Who says freshmen need time to adjust to college basketball? Not Johnson, who dazzled with a confidence, composure and athleticism throughout the week. He went coast-to-coast to dunk after a steal against Missouri, had seven rebounds against Kansas State and had 18 points and nine rebounds in the final against SDSU, grabbing two late steals and sealing the game with four free throws in the final 34 seconds.

The quote: “To win the championship here at the Maui Invitational, you need great players, and you need players that rise up to a challenge. (Johnson and Hollis-Jefferson) earned their all-tournament accolades by their performance. Not their reputation, but how they played in these three games in three days. So we leave here feeling very good about what we accomplished.� — Miller

The scene: Having inherited tickets to the Maui Invitational upon his April 2009 hiring, Miller persuaded guard Nic Wise to stay for his senior season and added a spring recruiting class that just so happened to include eventual No. 2 NBA draft pick Derrick Williams.

The games:

Wisconsin 65, ÃÛèÖÖ±²¥ 61: Wise battled foul trouble throughout a hard-played game that featured 54 fouls. Williams led the Wildcats with 25 points in what was only his second game as a starter.

ÃÛèÖÖ±²¥ 91, Colorado 87 (overtime): ÃÛèÖÖ±²¥ woke up just seven hours after returning to its hotel following the late Wisconsin game to begin preparing for the consolation bracket. The lack of sleep, and the Princeton-style backdoor cuts the Buffs used in their final season before Tad Boyle took over, challenged the Wildcats to stay awake. Wise rescued them with a career-high 30 points, making 5 of 9 3-pointers.

Vanderbilt 84, ÃÛèÖÖ±²¥ 72: Williams played just 14 minutes before fouling out, Jamelle Horne was 0 for 5 from 3-point territory and Miller was called for a technical foul after reminding officials to watch for three-second defensive violations. Then there was this: The 24th-ranked Commodores shot 53.4 percent from the field.

The discovery: Williams took the first step toward becoming the No. 2 pick in the 2011 NBA Draft. Against Wisconsin, he skillfully twisted and turned to pick up so many fouls he tied a UA record by going to the free throw line 21 times. And after starting Kyryl Natyazhko in the season opener, UA coaches knew they had a budding star.

The quote: “In my opinion, we probably learned more about ourselves as a team than any team in this tournament. … Offensively, we showed a lot of promise. We have some things to learn there but clearly, when you look at our offensive numbers through three games we’re better on that side of the ball than we are on defense. We’ll have to keep working to get better.� — Miller