Given an array of pairs $$$p[]$$$ of length $$$n(\leq 100000)$$$ I want to do the following:

Task 1: Given $$$q(\leq 100000)$$$ queries and $$$L,R,(pair\ p)$$$, output the number of pairs < p in the range $$$[L,R]$$$.

Task 2: Count the number of inversions in it. I can do inversions += query(i+1,n,p[i]) (if answer to Task 1 is available).

Task 3: Same as Task 1, but $$$L=1,R=n$$$ always. Can we directly use lower_bound for pairs < operator somehow?

< operator for pairs is defined as follows:- < (p1,p2){ return p1.F<p2.F && p1.S<p2.S;}

I know that we can do Task 1 for integers using a mergeSort-Tree, but how to do it for pairs?

Please let me know if there is an easier solution for Task 2 or Task 3 separately having an easier/direct implementation or smaller Time Complexity.