Let \( a_n \) be a real sequence with positive terms such that \( \displaystyle \lim_{n\to \infty} a_n = 0 \).

If the sequence \( c_n = a_n - a_{n+1} \) is nonincreasing, what is the strongest statement we can make about the limit \( \displaystyle \lim_{n\to \infty} n c_n \) (that is true for any choice of \( a_n \))?

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