A video sequence is to be encoded using H$\mathrm{.}263$ in PB$-$mode, This video has a frame size of $4$CIF $(704$x $576),$ chroma subsampling of $4$:$2$:$0,$ frame rate of $30$ fps$,$ and video length of $90$ minutes. The following is known about the compression parameters: on average, two I$-$frames are encoded per second. The video at the required quality has an I$-$frame average compression ratio of $10$:$1,$ an average P$-$frame compression ratio twice as good as I$-$frame, and an average B$-$frame compression ratio twice as good as P$-$frame. Assume that the P and B frames always come in pairs. Also assume that the compression parameters include all necassary headers and assume that $8$ bits are used per pixel, calculate the encoded video size.