Estimation of a logarithmic sum

Question

I need to estimate the sum $$ \underset{r=2}{\overset{t}{\sum}}\left(\frac{\log\log r}{r}\right)^{2}. $$ I tried to use the Abel's partial summation, and I got $$ \frac{(\log\log t)^{2}}{t}-\int_{2}^{t}\frac{2\log\log r}{r^{2}\log r}dr+\int_{2}^{t}\frac{2(\log\log r)^{2}}{r^{2}}dr $$ but I don't know how I can estimate the integrals. I would like to get an estimation like $$\underset{r=2}{\overset{t}{\sum}}\left(\frac{\log\log r}{r}\right)^{2}=O\left(\frac{\left(\log\log t\right)^{2}}{t}\right)$$ or something smaller. Thank you!