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Let NNN be the smallest positive integer for which 11+12+13+⋯+1N>100.\frac{1}{1}+ \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{N} > 100.11+21+31+⋯+N1>100. How many digits does NNN have?
Note: log10e≈0.434.\log_{10}e \approx 0.434.log10e≈0.434.
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