Converting a Pandas GroupBy multiindex output from Series back to DataFrame

I have a dataframe:

   City     Name
0   Seattle    Alice
1   Seattle      Bob
2  Portland  Mallory
3   Seattle  Mallory
4   Seattle      Bob
5  Portland  Mallory

I perform the following grouping:

g1 = df1.groupby(["Name", "City"]).count()

which when printed looks like:

                  City  Name
Name    City
Alice   Seattle      1     1
Bob     Seattle      2     2
Mallory Portland     2     2
        Seattle      1     1

But what I want eventually is another DataFrame object that contains all the rows in the GroupBy object. In other words I want to get the following result:

                  City  Name
Name    City
Alice   Seattle      1     1
Bob     Seattle      2     2
Mallory Portland     2     2
Mallory Seattle      1     1

How do I do it?