Leilani placed a digit in each of these 16 squares:

+------+------+------+------+
|      |      |      |      |      
+---- -+------+------+------+
|      |      |      |      |     
+------+------+------+------+
|      |      |      |      |     
+------+------+------+------+
|      |      |      |      |      
+------+------+------+------+

When she had finished, the grid had the following properties:

• No digit occured more than once in any row.
• The sum of the four digits in each row was the same.
• The sum of the four digits in each column was the same.
• Each row formed a different four-digit perfect square.

Complete the 4x4 square grid given above.

Note: Adapted from Enigma #1553 which appeared in 'New Scientist' in 2009.