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Read the following information carefully and answer the question based on that.

Two teams of five each must be selected from a group of ten persons. $\text{A}$ through $\text{J}$ of which $\text{A, E}$ and $\text{G}$ are doctors; $\text{D, H}$ and $\text{J}$ are lawyers; $\text{B}$ and $\text{I}$ are engineers; $\text{C}$ and $\text{F}$ are managers. It is also known that

1. every team must contain persons of each of the four professions
2. $\text{C}$ and $\text{H}$ cannot be selected together.
3. $\text{I}$ cannot be selected into a team with two lawyers.
4. $\text{J}$ cannot be in a team with two doctors.
5. $\text{A}$ and $\text{D}$ cannot be selected together.

Who among the following cannot be in the same team as $\text{I}?$

1. $\text{H}$
2. $\text{J}$
3. $\text{C}$
4. $\text{F}$