Q $3.[30$ Points$]$ Give a DPDA for the following languages:

i$)L_1=L(a^{*}a{b}^{*}b).$

ii$)L_2=\{wb{w}^R|win(ab{)}^{*}\}.$

iii$)L_3=\{wa{w}^R|win(ab{)}^{*}\}($Hint$.$ see A$2)$

Please do not use chat GPT$.$ Solve it by yourself and make the diagram. And explain each step