Hi Ioannis...Your plant could be either Persicaria lapathifolia
http://commons.wikimedia.org/wiki/File:Persicaria.lapathifolia.6994.jpg
or a Persicaria maculosa
http://commons.wikimedia.org/wiki/File:Redshank_(Persicaria_maculosa)_-_geograph.org.uk_-_1144064.jpg
(It looks more like a Persicaria lapathifolia to me, but I haven't seen the whole plant, so I can't tell for sure...Since it's in your balcony, you can check it your self :)
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