Pivot Table and Grouping on 2 Date Columns at Parallel Level

[Romi Kishore]

Consider the data as follows.

Region Date1 Number1 Date2 Number2
RegionA Feb-2011 2 Apr-2011 3
RegionA Feb-2011 1 Apr-2011 2
RegionA Mar-2011 1 May-2011 2
RegionA May-2011 1 Jul-2011 2
RegionA May-2011 1 Jul-2011 2
RegionA May-2011 1 Jul-2011 2
RegionA May-2011 2 Jul-2011 3
RegionB May-2011 1 Jul-2011 2
RegionB May-2011 1 Jul-2011 2
RegionB May-2011 1 Jul-2011 2
RegionC May-2011 2 Jul-2011 3
RegionC May-2011 2 Jul-2011 3
RegionC Feb-2011 5 Apr-2011 6
RegionC Aug-2011 5 Oct-2011 6

I want to group the data based on Date1 and Date2 columns (grouped as Months) on columns and Regions in Rows, whereas the numbers should be summed up. But the key part of the puzzle is that Date1 and Date2 columns should be one (at parallel level) after the other and NOT one under the other. Can this be done in Excel? And of course, the Number1 should be linked with Date1 and Number2 with Date2.