It was impossible to get rid of the people entirely from the frame so instead of fighting with them, I decided to use them to my advantage. I used long exposure to turn the majority of them into "ghosts". I love this effect because this way photo doesn't freeze a moment any more. It instead freezes period of time (like a few seconds video compressed into one still image). It is evidence of time passing by.
Only people staying almost completely still throughout the exposure appeared in the final shot. And ones that appeared look pretty cool as they take a photo with a flash! Not only it adds some additional light on them but also looks pretty interesting.
Camera: Canon 5D MK II
Lens: Canon 24-105 f/4 L IS USM
Focal length: 28 mm
Exposure time: 10 s ("middle" exposure)
Number of exposures: 7
E.V. Step: 1
Flash used: no
Software: Magic Lantern 2.3, Lightroom 4.2, Photoshop CS6