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Harvey Fierstein, Andrew Rannells, Michael Urie, Roger Rees, Jonathan Groff, Laura Benanti: All of these familiar Broadway faces, and a ton more, got together to put on a show. Making the rounds online ahead of the Sochi Winter Olympics, “Russian Broadway Shut Down,” a YouTube musical comedy about gays in Russia, stars a cast of what seems like thousands in a parody so intricately produced that it prompts the question: How’d they do that?

The seg imagines an alternate-universe Broadway in Mother Russia, where everyone speaks like Boris and Natasha and wears giant fur hats. In accordance with its gay propaganda laws, the government has ordered homosexual content taken out of all musical theater — “Glitter and be sexually conventional,” sings Rialto regular Rebecca Luker — before it shuts down the Great Red Way completely. The Broadway-in-Russia community responds, natch, by putting on a show — an agit-prop tuner called “Love and Punishment.”

The video is the work of a circle of Broadway denizens who know each other, and seemingly everyone else, though their overlapping resumes. Off Broadway actor John Walton West (“Newsical,” “The Last Smoker in America”) directs;  Jason Michael Snow, a cast member of “The Book of Mormon,” composes;  Simon Pearl (“Les Miserables”) filmed and edited; Cody Williams (“Cinderella”) produced. All four are on a ten-person team, including “The Drowsy Chaperone” co-composer/lyricist Lisa Lambert, all credited as exec producers and writers.

West had teamed before with many of those collaborators on a handful of Broadway-themed comedy videos in the past, including a “Smash”/reality-TV mashup and a musical episode of “Downton Abbey.” Spurred by the controversy of Russia’s homosexual propaganda laws — as well as West’s experience with current events comedy “Newsical” — the group decided to tackle a weightier theme this time around.

The new video turns heads with its length (nearly 12 minutes), its wealth of original songs and a cast of more than 100 that encompasses not just actors —  Jackie Hoffman, Jeremy Jordan, Michael Cerveris — but seemingly every facet of the Broadway industry, including composer Andrew Lippa, costume designer William Ivey Long, journo Michael Musto, producer Robyn Goodman and directors David Cromer and Casey Nicholaw. For the kind of YouTube comedy that’s usually put together as a lark, it looks like it cost a relative fortune.

It didn’t. But if the overall production cost of the seg was “minimal,” according to West, it went way over-budget in terms of time: When the creators concocted the idea back in October, they imagined they’d crank it out in a couple of days and release it in November. Instead it hit YouTube in late January.

The problem was coordinating schedules, as more and more familiar (and in-demand) names signed on to the project to support the cause. All creatives participated pro bono, and costs were further kept down when filming locations were either donated or rented at a discount.

Some money had to be shelled out for a recording studio, but otherwise the video was entirely a boostrapped affair. One big-group musical number, for instance, was performed by the cast of a workshop of the upcoming revival of “On the Town,” who showed up en masse to shoot the sequence during a lunch break.

Since it was posted Jan. 23, the video has attracted attention not just in the Gotham theater industry but in Russia as well. The comments section is packed with debate, if that’s not too fine a word for it, from both sides of the issue.

The fact that it’s stirring up talk means it’s doing it’s job, according to its creators. Everyone is all for parlaying their multi-hyphenate skills into paying gigs, but “Russian Broadway Shut Down” was put together as a socially engaged but fun side project, not as a calling card for future employment.

“One of the thing that’s been the most fun about this has been the lack of that pressure behind it,” West said.