Hello! I have been stuck on this problem for a while, here is what it asks:

"Given an array say if it is possible to choose a set of different subarrays of length 2 such that every index is taken at least once."

For example $$$[1, 2, 1, 2, 3]$$$ we can choose $$$[1,2], [2,1], [2,3]$$$ corresponding to the indices $$$[1,2], [2,3], [4,5]$$$ (indexed from $$$1$$$). The problem is this one: https://codeforces.com/gym/103999/problem/D

I have heard that this is solvable with $2$SAT?, but I have no ideea how. I have never solved a $2$SAT problem similar to this one, and I don't know what I am missing, basically I don't get how I can construct a graph such that it solves this tasks.

Any help, similar problem(s) or hints would be much appreciated thanks!