Suppose a player will navigate a dungeon (map provided below) with the following rules. The player must get from the entrance to the exit, and the player must conquer a room before being allowed to pass on to the next. The probability the player will conquer a room is indicated on the map (and conquering the rooms are independent events). The player must conquer Room A and Room B to move forward. Next, as long as the player conquers at least one of Room C1 or Room C2, the player can move forward. Finally, the player must conquer at least one of Room D1 or Room D2 to reach the exit. Under these rules, what is the probability the player will reach the exit? (Decimal form, rounded to four places.)