Find the Upper Bound

Algebra Level 3

There exists a smallest possible positive integer \(N\) such that \[\dfrac{(x_1+2x_2+\cdots +2014x_{2014})^2}{x_1^2+x_2^2+\cdots +x_{2014}^2}\le N\] for all real sequences \(\large \{x_i\}_{i=1}^{2014}\). Find the sum of the digits of \(N\).

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