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There exists a smallest possible positive integer NNN such that
(x1+2x2+⋯+2014x2014)2x12+x22+⋯+x20142≤N\dfrac{(x_1+2x_2+\cdots +2014x_{2014})^2}{x_1^2+x_2^2+\cdots +x_{2014}^2}\le Nx12+x22+⋯+x20142(x1+2x2+⋯+2014x2014)2≤N
for all real sequences {xi}i=12014\large \{x_i\}_{i=1}^{2014}{xi}i=12014.
Find the sum of digits of NNN.
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