Inversion Queries

You are given a permutation array $A$ of integers in the range $[1, N]$. Your task is to handle $Q$ queries of the following type: - Given $L$ and $R$, first create a new array $B$, also of length $N$, according to the following: - $B_i = L$ if $A_i < L$. - $B_i = A_i$ if $L \le A_i \le R$ - $B_i = R$ if $R < A_i$. - Find the number of inversions$^{\dagger}$ in $B$. --- $^{\dagger}$ A