Given a system enforcing a strict password policy requiring a minimum length $14$ characters, including at least one uppercase letter $($A$-$Z$)$ one digit $(0-5),$ and one special character $($~$,^,$ @$,$ #$,$ $$,\%,$ & $*,\_,),$calculate the total number of possible passwords adhering to these requirements for an exact length of $8$ characters.

$1-$ Calculate the entropy of passwords conforming to this policy, considering the specified character set and length constraints.

$2-$ Determine the total count of possible passwords meeting this policy criteria

$3$

Compute the change in password strength variance if the policy is modified to allow longer passwords minimum length of $16$ characters$)$ but restricts the characteret to only lowercase letters $($a$-$z$).$

$4-$ Explain the importance of entropy and variance in relation to the security implications of this password policy against brute$-$force attacks