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stable_sort
template<class RanIt>
    void stable_sort(RanIt first, RanIt last);
template<class RanIt, class Pred>
    void stable_sort(RanIt first, RanIt last, Pred pr);
The first template function reorders the sequence designated by iterators in the range [first, last) to form a sequence ordered byoperator<. It does so without altering the relative order of elements that have equivalent ordering. Thus, the elements are sorted in ascending order.
The function evaluates the ordering predicate X < Y at most ceil((last - first) * log2(last - first)) times. (Given enough temporary storage, it can evaluate the predicate ceil((last - first) * log(last - first)) times, at most.)
The second template function behaves the same, except that it replaces operator<(X, Y) with pr(X, Y).