The letter E can be constructed of rectangles one unit wide and unit squares as in the following:

+---------+
|         |
+--+------+
|  |
+--+--+
|  |><|
+--+--+
|  |
+--+------+
|         |
+---------+

Find the length of the top and bottom vertical rectangles such that the center of gravity of the letter is exactly at the center of the middle square.