In Professor Layton and the Unwound future how does the prime minister get kidnapped?

I know that Dimitri kidnapped them, but how did they just "diappear"?In Professor Layton and the Unwound future how does the prime minister get kidnapped?
As is typical of the Layton series, not everything is explained in detail



While the game tells us that the prime minister "was abducted by Dimitri and is now being held prisoner", it doesn't provide a flashback showing exactly how this was achieved



When the prime minister is revealed as being held prisoner, a number of significant plot twists have just occurred and it would seem unnatural for Dimitri (in a situation where he's in a rush to get away) to take the time to unnecessarily explain how the abduction was achieved when all that really matters (at the time) is that the prime minister was abducted



It's therefore up to the player to speculate how this could've been done (albeit that the cut scene shows both Dimitri and the prime minister only inches away from being killed)



Given that the time machine backs onto trees (it's not surrounded by the audience), the prime minister could've been removed through a secret back panel and quickly taken through the trees to, say, a waiting car while everyone was distracted by the explosion



The scientists who also went missing during the demonstration could've easily been taken earlier or taken after the explosion under the pretence of being guided to safety

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