A $\text{200 mV}$ full scale dual-slope $3\frac{1}{2}$ digit $DMM$ has a reference voltage of $\text{100 mV}$ and a first integration time of $\text{100 ms}$. For an input of $[100+10 \cos (100\pi t)]mV$, the conversion time (without taking the auto-zero phase time into consideration) in $\text{millisecond}$ is $\_\_\_\_\_\_\_$.