A confusing detail about the Most Vexing Parse

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My question is how the following line can be parsed as a function declaration:

vector<int> v(istream_iterator<int>(cin), istream_iterator<int>());

I understand most of the details of the Most Vexing Parse and why the second temporary iterator can be interpreted as a type that is a function returning an iterator and taking no arguments, but what I don't get is why the first temporary iterator can be interpreted as a type. What type does it represent? My thought is that it would be some sort of function type, but I can't see how the name cin gets used. Is it declaring that the parameter is an istream_iterator<int> named cin? If so, does that mean that you can arbitrarily parenthesize the names of arguments to functions? And if so, why?

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