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Yes, this is indeed a legal connection - just.

Whether it's "very tight" or just "tight" depends on where you are flying in from. If it's from within the Schengen area (as your handle suggests it might be!) you shouldn't have a problem as the gates are likely to be close to each other and you won't have to re-clear security.

If it's from further afield (such as North America) things could be a bit tricky as you need to get from one end of the airport to the other AND re-clear security.