Find the smallest positive integer $n$ with the following property:  for every sequence of positive integers $a_1,a_2,\ldots , a_n$ with $a_1+a_2+\ldots +a_n=2013$, there exist some (possibly one) consecutive term(s) in the sequence that add up to $70$.

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