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It's already a thing - discovered it in the women's loos at a venue I went to recently - just that it is much more compact than the average bin, and therefore you don't have that horrible sensation of your thigh against the bin 
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In Denmark (of course in Denmark, its always Denmark, they are so grown up.... ) they have a neat little plastic bag sealed by a wide clip attached to the wall. Replaced frequently. Simples.pic.twitter.com/2MFdVoCHut
