If $S_n=\frac{e^{1/n}}{n^2}+\frac{2}{n^2}{e}^{2/n}+\frac{3}{n^2}{e}^{3/n}+\cdots +\frac{1}{n}e$ then $\underset{n\to \mathrm{\infty }}{lim} S_n$ is

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