– Virginia coach Tony Bennett brought a prop to the NCAA basketball tournament — a stuffed monkey, which he used to drive home a point about the pressure his program felt after making dubious history last season.

Last year Bennett’s team became the first No. 1 seed in NCAA tournament history to lose to a No. 16 seed, a 20-point embarrassment to Maryland-Baltimore County.

Armed with a No. 1 seed again, Virginia played tight and trailed by double digits against Gardner-Webb in the first game of this tournament before pulling away to win and advance.

The Cavaliers ousted Oklahoma in the second round, prompting Bennett to walk into the locker room with the stuffed monkey on his back and yank it off in celebration.

Cue laughter. And relief.

“Only those of us who have been part of last year’s team and been through this year … can appreciate it,” Bennett said.

The Purdue Boilermakers have some idea. They’re trying to get a similar monkey off their back.

Bennett and Purdue coach Matt Painter are two of the most respected coaches in college basketball because they have built model programs that develop players and win consistently. But a piece is missing from their résumés: a Final Four appearance.

One of them will remove that asterisk Saturday in the South Regional final. The winner won’t have to answer that question anymore. The “yeah but” retort to their run of success will be gone for good.

“Going through what we did, it created a fire in me that wanted to become a better coach and pursue trying to get these guys as far as they can — a Final Four, national championship,” Bennett said. “It’s burning hot, but it did something maybe as significant or greater. It made me realize that if that never does happen, I’ll still be OK.”

That’s true. Their programs likely will continue to hum along because they were constructed with a solid foundation. Painter and Bennett recruit players who fit their systems and style of play and personality. Each program has an unmistakable identity and blueprint.

Their tournament history shows that March offers no guarantees.

Virginia has been a No. 1 seed four times under Bennett, who took over the Cavaliers program in 2009-10 and has won 175 games in the past six seasons. The Cavs have advanced as far as the Elite Eight only twice in that span, counting this year.

Painter, who took over from legendary Gene Keady in 2005-06, has guided Purdue to three Big Ten championships, 11 NCAA tournament appearances and five trips to the Sweet 16. Consistent, but still waiting for that next step.

“We have a lot of guys who have sacrificed through the years and had really, really good seasons, but you haven’t been able to put that cherry on the top and get to a Final Four,” Painter said. “I think that would be great for a lot of people that have Purdue blood in them.”

Tournament success often depends on matchups. One cold shooting performance can result in an early exit. And sometimes luck — or bad luck — plays a factor.

Purdue was ranked No. 3 nationally in 2010 when forward Robbie Hummel suffered a torn ACL in a game against the Gophers in late February. His injury doomed the Boilermakers’ postseason hopes.

Virginia’s defense-first, methodical style of play results in criticism of Bennett with each tournament flameout.

“I don’t know why it’s a Tony thing because he brought UVA from the dirt,” Cavs star guard Kyle Guy said. “[We] haven’t been to a Final Four since, what, ’84? So it’s not just him. Coach Painter is a fantastic coach, as is Coach Bennett. And neither of them has been to the Final Four. Sometimes the ball just doesn’t bounce your way.”

Virginia’s players and coaches have faced what probably feels like a million questions about last season’s loss to UMBC and previous tournament failures. Neither program needs validation, but a Final Four appearance would be a sweet reward for two teams that are consistently excellent but eager to take that next big step.

“Burdened, unburdened, doesn’t really matter in my opinion,” Bennett said. “You just step up to the challenge that’s there.”