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?
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