Ash writes the positive integers from $1$ to $2016$ inclusive as a single positive integer $n = 1234567891011\ldots2016$. What is the result obtained by successively adding and subtracting the digits of $n$? In other words, compute $1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 1 + 0 - 1 + \ldots$.

Let's think step by step and output the final answer within \boxed{}.
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