q₁ and q_n are two queries.
Let f₁, ..., f_n-1 be n-1 transformations such that
f₁(q₁) = q₂, f₂(q₂) = q₃, ..., f_n-1(q_n-1) = q_n.
The distance d(q₁,q_n) between two queries
q₁ and q_n is defined as:

where w_j is the weight for transformation step f_j