JEE Advanced 2018 - 3

There are five students $S_{1}$ , $S_{2}$ , $S_{3}$ , $S_{4}$ and $S_{5}$ in a music class and for them there are five seats $R_{1}$ , $R_{2}$ , $R_{3}$ , $R_{4}$ and $R_{5}$ arranged in a row, where initially the seat $R_{i}$ is allotted to the student $S_{i},i = 1, 2, 3, 4, 5$ . But, on the examination day, the five students are randomly allotted the five seats.

For $i = 1, 2, 3, 4$ , let $T_{i}$ denote the event that the students $S_{i}$ and $S_{i+1}$ do NOT sit adjacent to each other on the day of the examination. Then the probability of the event $T_{1}\cap T_{2}\cap T_{3}\cap T_{4}$ is $\frac{A}{B}$ where $A,B$ are co-prime integers. Find $A+B$