Given the following language: $\{a^n{b}^m{a}^n{b}^m\}.$ Prove whether it is regular or nonregular. If regular, show FA$.$ If nonregular, prove using the pumping lemma by showing how many partitions are possible for $Y$ part and for each $Y$ part, show whether it supports the regular language property or not.

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Build a context free grammar for this language. Do not use null $({?}^{{?}^{?}})$ production. Show leftmost derivations for two valid strings.