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Answer the questions on the basis of the following information.

Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answer-key. All the others create their answer-key from one or two people who already possess the same. These people are called his/her “sources”. If the person has two sources, then he/she compares the answer-keys obtained from both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source’s answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.

The paper contained $200$ questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.

Name

Wrong Answer(s)

Blank answer(s)

A

46

--

B

96

46, 90, 25

C

27, 56

17, 46, 90

D

17

--

E

46, 90

--

F

14, 46

92, 90

G

25

--

H

46, 92

--

I

27

17, 26, 90

How many people (excluding the mastermind) needed to make answer before C could make his answer key?

  1. $2$
  2. $3$
  3. $4$
  4. $5$
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