No school has made more Final Four appearances without winning a championship than Houston.During their six previous Final Four forays, the Cougars have lost to legends like Kareem Abdul-Jabbar and Patrick Ewing and they’ve lost in legendary fashion — specifically Lorenzo Charles’ last-second dunk that enabled North Carolina State to stun Hakeem Olajuwon, Clyde Drexler and the rest of Phi Slama Jama in the 1983 NCAA title game.Despite dominating the Big 12 and losing just once since Thanksgiving weekend, Houston (35-4) wasn’t necessarily supposed to reach Monday night’s NCAA championship game against Florida (35-4) in San Antonio.Houston’s chances looked particularly dire when the team trailed by 14 with eight minutes to go in Saturday’s semifinal and by six — without the ball — with just over one minute to play.But now that the Cougars have produced a legendary comeback to knock off the nation’s No. 1 team (Duke) featuring college basketball’s No. 1 player (Cooper Flagg) leading the nation’s No. 1 offense over the last 25 years (per KenPom’s efficiency ratings), can they take it the final step and let some other school become known as the best to never win a championship?And with Olajuwon, Drexler, Elvin Hayes and other legendary Houston alums watching from the Alamodome’s best seats?”I’m sure (Olajuwon) poured his heart and soul into this program, just like a lot of the guys that came before us,” said Cougars senior LJ Cryer, who scored a team-high 26 points in Saturday’s upset and leads Houston with 15.6 points per game. “We’re standing on those guys’ shoulders, everyone who came before us. It would mean a lot to get this done. Not only for us, but for them.”Houston, which has won 18 straight, also has designs on making 69-year-old Kelvin Sampson the oldest coach to win an NCAA championship. Sampson is the architect of the Cougars’ system focused on defense, rebounding and toughness, though this year’s group also leads the nation in 3-point shooting (39.9 percent) thanks to guards Cryer, Emanuel Sharp (12.8 ppg) and Milos Uzan (11.5 ppg).”Last night, I got so many texts,” Sampson said. “I saw Tubby (Smith) and Rick Barnes, Tom Izzo, (Gregg Popovich), a bunch of the older coaches. They all kind of had similar messages to me: Win one for the old guys, something like that.”To do so, Houston and its national-best defense will have to solve an athletic and analytic juggernaut developed by one of Division I’s youngest head coaches, 39-year-old Todd Golden.The Gators feature not only the third-most efficient offense in the KenPom era — averaging 128.8 points per 100 possessions, just shy of Duke’s 130.0 rating — but they also boast the NCAA Tournament’s hottest player in senior point guard Walter Clayton Jr.When Florida needed to rally from 10 points down to Texas Tech with five minutes to play in the West Region final on March 29, Clayton reeled off 13 of his game-high 30 points. When Florida needed to come back from eight points down to Auburn in Saturday’s semifinal, the first-team All-American poured in 20 of his career-high 34.