Problem link I can't understand why the solution to thee problem is reducible to min-cut.Can anyone provide the intution behind it?

Given an array how to find sum of all f(A',k) where A' is subarray of A(original array) and f(A',k) are total unordered pairs (i,j) such that abs(A[i]−A[j])>=k.How to solve this using segment tree.What should be the merge function? Problem link :Problem link