How to approach this problem 3-D Structure?

#1

Not getting initial thought.
Where BIT will be fit here?
I am completely blank.
Kindly provide hint.

#2

there are N3 points <= 10^6, so it is possible to store the value at every point
also, any volume in space can be expressed in terms of volume (1,1,1) (x,y,z)
so this is where BIT comes into picture. if you can find volume between (1,1,1) and (x,y,z) efficiently,
you can find out any volume (x1,y1,z1) (x2,y2,z2)

#3

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