+----+----+----+----+
| 23 |    |    |    | 
+----+----+----+----+
|    |    | 64 |    |
+----+----+----+----+
|    |  N |    |    | 
+----+----+----+----+
|    |    |    |101 |  
+----+----+----+----+

In the 4x4 grid provided above:

• Each the 16 values appearing in the 16 cells is a positive integer.
• The 4 values corresponding to each of the 4 rows are in arithmetic sequence.
• The 4 values corresponding to each of the 4 columns are in arithmetic sequence.

Determine the total number of distinct positive integer values that N can assume.