For an increasing geometric sequence $a_1,a_2,\mathrm{....}{a}_n$ if  $a_6=4a_4$  and  $a_9-a_7=192$ and  $\sum _{i=4}^n{a}_i=1016$  then n =_______

$$\begin{gathered} a_6=4a_4 \\ {a}_1{r}^5=4a_1{r}^3 \\ r^5-4r^3=0 \\ {r}^3(r^2-4)=0 \\ r=2 (\because r>0) \\ {a}_9-a_7=192 \\ {a}_1{r}^8-a_1.r^6=192 \\ {a}_1{r}^6(r^2-1)=192 \\ {a}_1\left(64\right)\times 3=192 \\ {a}_1=1 \\ \sum _{i=4}^n{a}_i=1016 \\ {a}_4+a_5+\mathrm{.....}+a_n=1016 \\ {a}_n-(a_1+a_2+a_3)=1016 \\ {2}^n-1=1016+1+2+4=1023 \\ {2}^n=1024n=10 \end{gathered}$$