Find the Upper Bound

Algebra Level 2

There exists a smallest possible positive integer NN such that

(x1+2x2++2014x2014)2x12+x22++x20142N\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 {xi}i=12014\large \{x_i\}_{i=1}^{2014}.

Find the sum of digits of NN.

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