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The peerless Swiss Cologna came home more than 18 seconds ahead of Norway's Simen Hegstad Krueger, who took silver from the Russian Denis Spitsov.
It was Cologna's fourth Olympic cross-country gold medal in all, stretching back to his first at the 2010 Vancouver Games.
At the other end of the race, the popular Taufatofua -- famed for appearing at the freezing opening ceremony with his chest exposed to the elements -- finished in 114th place.
Last, two spots farther back, was the Mexican German Madrazo, who completed the race to loud cheers from the crowd while proudly brandishing a large Mexican flag.