Let language $L_1=\{a^n{b}^{n+m}{c}^m$:$n,m0\}$

i$.(10$ points$)$ Construct a context$-$free grammar for $L_1$ using $S$ as the start symbol.

ii$.(3$ points$)$ Give the $4-$tuple of the CFG$.$

iii. $(5$ points$)$ Using your grammar, construct a parse tree for the sentence aabbbbcc.

iv$.(2$ points$)$Is your grammar ambiguous?

v$.(10$ points$)$ Construct a pda for $L_1.$

vi$.(5$ points$)$Be sure to to give the septuple as well as transitions functions.