HMMT 2013 U33

Compute the value of $1^{25}+2^{24}+3^{23}+\ldots+24^{2}+25^{1}$. If your answer is $A$ and the correct answer is $C$, then your score on this problem will be $\left\lfloor 25 \min \left(\left(\frac{A}{C}\right)^{2},\left(\frac{C}{A}\right)^{2}\right)\right\rfloor$.