Our overall approach should be to consider each possible substring of ~S~, check whether or not it's redundant, assemble a list of distinct substrings which are, and output the number of substrings in this list at the end.

We can do so by iterating over all pairs of indices ~(i, j)~, such that ~1 \le i < j \le |S|~. Each such pair corresponds to the substring ~S_{i \dots j}~, with a length of ~L = j-i+1~. We can then consider each index ~k~ between ~i+1~ and ~j~ (inclusive), and check if the substring ~S_{k \dots (k+L-1)}~ is equal to ~S_{i \dots j}~ (note that ~k~ should also be capped at ~|S|-L+1~ to avoid considering substrings which would go past the end of ~S~). If such an index ~k~ is found, then a pair of overlapping equal substrings has also been found, meaning that ~S_{i \dots j}~ must be redundant.

What remains is maintaining the list of distinct redundant substrings, and being able to add ~S_{i \dots j}~ to it if not already present. One option is to maintain this list as an array, and loop over all of its existing entries to check if ~S_{i \dots j}~ is equal to any of them. A more elegant option is to use a built-in data structure such as a C++ set, which will automatically ensure that its entries are all distinct.

The time complexity of the solution described above is ~\mathcal O(N^4)~, which is comfortably fast enough, though it's also possible to optimize it to ~\mathcal O(N^3)~.