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
- every team must contain persons of each of the four professions
- $\text{C}$ and $\text{H}$ cannot be selected together.
- $\text{I}$ cannot be selected into a team with two lawyers.
- $\text{J}$ cannot be in a team with two doctors.
- $\text{A}$ and $\text{D}$ cannot be selected together.
Who among the following cannot be in the same team as $\text{I}?$
- $\text{H}$
- $\text{J}$
- $\text{C}$
- $\text{F}$