Add a plus or minus sign randomly between 1-2011 consecutive natural numbers (but the result should be positive), is the result odd or even? Be detailed!

First of all, be clear
Odd + - odd = even
Even + - odd = odd
Even + - even = even
Even numbers in the middle of 1-2011 don't matter
There are 1006 odd numbers
The 1006 are divided into 503 groups, and each group is even
The final result is even

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