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 digits of \(N\).

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