# Find the Upper Bound

Algebra Level 4

There exist 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 $$N$$.

×