Starting with the number $1$ and moving to the right in a clockwise direction a $5$ by $5$ spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is $101$.

What is the sum of the numbers on the diagonals in a $1001$ by $1001$ spiral formed in the same way?