$(20$pt$)$ For the snooping protocol which has three states of invalid, exclusive and shared, specify cache states in processors P$1,$ P$2,$ and P$3$ for each step. Assumes initial cache state is invalid. Specify the cache states and the directory state for directory$-$based protocol.

$\backslash$table$[[$step$,$P$1$ cache state,P$2$ cache state,P$3$ cache state,Directory state for A$1,],[$P$1$: read A$1,,,,,],[$P$1$: write $1$ to A$1,,,,,],[$P$1$: read A$1,,,,,],[$P$2$: write $2$ to A$1,,,,,],[$P$3$: read A$1,,,,,],[$P$2$: write $3$ to A$1,,,,,],[$P$2$: write $0$ to A$1,,,,,],[$P$1$: read A$1,,,,,],[$P$1$: write $1$ to A$1,,,,,]]$