BEIJING - It was nice just to play a game, U.S. women's hockey players said before the Olympics began.

It didn't matter that, aside from going at each other in practice over the past several months, the only other competition they had was Canada during an exhibition tour that was cut short by COVID-19.

Facing strange and different teams, in a strange and different country, at the Olympics was a good thing. At least that was the idea.

In less than a week of games at the Wukesong Sports Center, it quickly has been made clear that it's again all about the U.S. and Canada in this tournament. Everyone else is training fodder.

After laying waste to fellow Group A opponents, the next iron-sharpens-iron moment between the women's hockey behemoths comes on Tuesday (10:10 p.m. Monday in Minnesota; USA Network) when Team USA plays Canada in the final game of group play for both teams.

It shouldn't matter much. All five teams in Group A automatically advance to the quarterfinals and will be joined by the top three teams from Group B. So little is on the line.

But it does matter.

"I think that's the game everybody gets up for," said forward Hilary Knight, who scored twice on Sunday and now has nine goals in her Olympics career, tying her for fifth on Team USA's all-time list.

What else could possibly be learned from playing Canada, whom they played six times during the My Why Tour between October and December before the final three games were canceled?

Nothing. Just a hated rival.

"It could be on a pond, and you put two of those jerseys on, and certainly all of a sudden that the intensity ramps up," U.S. coach Joel Johnson said. "Even though both teams know that they're probably moving on, because of the format of the tournament. It's not even about the seeding.

"It's about the pride of for Canada wearing the maple leaf and for us wearing the red, white and blue. It just never gets old."

Team USA will enter the game after an 8-0 rout of Switzerland on Sunday that was over in the first period when the United States pumped in five goals. Switzerland was outshot 66-12 by an American team that was at peak form. Team USA is 3-0 in group play and has outscored opponents 18-2. And Johnson has given each of his goaltenders — Alex Cavallini, Maddie Rooney and Nicole Hensley — one start during group play.

The game against Switzerland came with a spotlight on St. Thomas, as Johnson — also the Tommies women's coach — faced two players who suited up for the Swiss.

Unfortunately for St. Thomas fans, eight different U.S. players scored a point in the first period against Switzerland goalie Saskia Maurer, who plays for the Tommies. In all, four players for Switzerland have Minnesota ties. Defender Nicole Vallario is Maurer's teammate at St. Thomas. Team captain Lara Stalder played at Minnesota Duluth, and Laura Zimmermann is a St. Cloud State signee.

Maurer was lifted after the first period.

"I was fortunate enough to see Nicole and Saskia walking off the ice," Johnson said. "And, and of course, they're disappointed as competitors would be and frustrated, and I said, 'Hey, it was just fun to be a part of this.'

"And they both looked at me like, 'I don't want to talk right now,' and 'And I loved it.' "

On to Canada, with no medal on the line yet, but plenty of motivation. Canada steamrolled Switzerland and Finland in its first two games, outscoring them 23-2.

Canada will be Team USA's biggest roadblock to winning gold in Beijing. But the Americans lost to Canada in group play four years ago in PyeongChang, South Korea, then knocked the Canadians off in overtime in the gold-medal game.

Sounds like the U.S. would prefer to win both meetings this time.

"They're a good team," Knight said. "A good team versus a good team. So we'll see. We'll see kind of where we stack up."