Consider a network containing $100$ hosts. Each host runs $3$ network applications $($a file sharing application, voice call application, and instant messaging application$),$ and each application should be able to communicate with the corresponding application on any other host $($e$.$g$.$ voice on host $1$ with voice on host $2$; but not voice on host $1$ with file sharing on host $2).$

A$)$ If host$-$level symmetric key security is required in the network, what is the maximum number of session keys needed?

B$)$ If application$-$level symmetric key security is required in the network $($for the $3$ applications$),$ what is the maximum number of session keys needed?

C$)$ If host$-$level Asymmetric key security is required in the network, what is the maximum number of session key needed?