Acceleration of a Three Block Atwood Machine | 3 Blocks 2 Pulleys, 2 Strings, no Friction

Three blocks are connected by light strings which pass over frictionless pulleys such that two of the blocks are hanging. The blocks are released from rest, calculate the acceleration of the system (all three blocks).
This variant of Atwoods Machine is unique in that the middle block does not accelerate due to gravity, instead it accelerates exclusively due to a difference in tensions between the two strings.
This problem commonly comes up in introductory physics courses including AP Physics 1, AP Physics C Mechanics and appears on exams such as A Levels and JEE.