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

An integer is written on each unit square of a 4×4 unit square chessboard given above.

The number in each unit square is equal to the sum of the numbers in all unit squares that share a common edge with that unit square.

What is the largest number of positive integers (out of the 16 numbers) that can be written on this chess board?