Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/ follow from the Statements, disregarding the commonly known facts:

Statement 1: Some doctors are teachers.
Statement 2: All teachers are engineers.
Statement 3: All engineers are scientists.

Conclusion I: Some scientists are doctors.
Conclusion II: All engineers are doctors.
Conclusion III: Some engineers are doctors.

Which one of the following is correct?