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Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of $13$ questions $\text{ (Q01 to Q13)}.$ Questions can be created by external “subject matter experts” $\text{(SMEs)}$ or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.

If a question is created by an $\text{SME},$ it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.

A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.

The following facts are known about the review process after its completion.

  1. $\text{Q02, Q06, Q09, Q11,}$ and $\text{Q12}$ were rejected and the other questions were accepted.
  2. Amal reviewed only $\text{Q02, Q03, Q04, Q06, Q08, Q10, Q11,}$ and $\text{Q13}.$
  3. Bimal reviewed only $\text{Q02, Q04, Q06}$ through $\text{Q09, Q12,}$ and $\text{Q13}.$
  4. Komal reviewed only $\text{Q01}$ through $\text{Q05, Q07, Q08, Q09, Q11,}$ and $\text{Q12}.$

How many questions were $\text{DEFINITELY}$ created by the $\text{SMEs}$?

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