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Katy Perry and her new man Justin Trudeau Tokyo drifted into each other's arms in Japan Monday ... and we have pics.

Trudeau joined his new girlfriend on the Japanese leg of her world tour, reportedly grabbing something to eat at a restaurant with its own live sumo wrestling show.

Tough to imagine the former Prime Minister of Canada going from addressing parliament to sitting ringside at a sumo match with his Grammy-nominated lady ... but when in Rome ... Gallery Launch Gallery Getty

And what does one wear to dinner and a sumo match? Trudeau went casual with jeans, a baseball cap, and black jacket, while Perry also donned a cap and cargo pants with a tan jacket and black face mask.

This marks one of their first outings together in their new relationship,

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