Double Substrings

A string is called a "Double" if it is of the form $X+X$ for some non-empty string $X$ where $+$ denotes the string concatenation operator. You are given a string $S$ and $Q$ queries of the form $[L, R]$. For each query, you need to calculate the sum of the lengths of all "Double" strings which are contained entirely within the range $[L, R]$, i.e. only consider substrings $[l, r]$ which