Describe the language generated by the following context$-$free grammar, using $S$ as the start symbol:

$S$aSb$|A|B$

$AaA||$

$BBb||$

A sequence of $a\text{'}$s of any length followed by a sequence of $b\text{'}$s of any length. For example, aaabb.

A sequence of $a\text{'}$s of any length followed by an equal length sequence of $b\text{'}$s$.$ For example, aaabbb.

Either a sequence of $a^{\text{'}}$ s followed by an equal length sequence of $b\text{'}$s; or a sequence of only $a^{\text{'}}$; or a sequence of only $b\text{'}$s$.$ For example, aabb or aaa or $bbb.$

An arbitrary sequence of $a^{\text{'}}$ s and $b\text{'}$s$,$ provided that the total number of $a\text{'}$s is the same as the total number of $b\text{'}$s$.$ For example, abaabb.