How to convert quaternion between coordinate systems

Question

I have a quaternion, coming from a system with the following: (Unity)

Left-handed.
Forward direction: Z axis
Right direction: X axis
Up direction: Y axis

I need to convert this into a coordinate system that is: (3ds max)

Right-handed.
Forward direction: Y axis
Right direction: X axis
Up direction: Z axis

I have tried negating the axis, and angle, I have tried switching values, I cannot get this to work. All help greatly appreciated! I am working in C#