Question 3A sequence of one hundred positive integers $x_1,x_2,x_3,\ldots,x_{100}$ are such that $$(x_1)^2+(2x_2)^2+(3x_3)^2+\cdots+(100x_{100})^2=338350.$$ Find the largest possible value of $x_1+x_2+\cdots+x_{100}$.