I was doing this problem and was getting TLE on the last two test cases.
On a whim, I decided to replace my sort() functions with stable_sort(), and the solution passed.
According to this benchmark, stable_sort uses less iterations overall in g++ 5.3.0 and clang++ 3.7.0 than sort on average.
In the problem I sorted a vector<pair<int, pair<int,int>>>, which would take up to three comparisons each time. I considered this a possibility for the lower constant factor of stable_sort for this problem, but was not able to replicate the results.
You can try to submit my solution and it should AC. But if you replace "stable_sort" with "sort" it will TLE.
Does anyone know which types of cases stable_sort can outperform sort?