Dates can be writen as an $$8$$-digit number in the form $$y$$ $$y$$ $$y$$ $$y$$ $$m$$ $$m$$ $$d$$ $$d$$. For example, $$20140125$$ stands for January $$25^{}\text{th}$$ $$2014$$. How many days are there in the year $$2014$$ such that its $$8$$-digit representation contains equal numbers of digit $$0$$, $$1$$ and $$2$$? 
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