Construct a DFA that recognizes the language that is the union of the languages from DFA $1$ and DFA $2.$

DFA $1$:

$1)$ q$0$: input $1$ goes to q$1,$ input $0$ goes to q$2$

$2)$ q$1$: input $0,1$ goes to q$2$

$3)$ q$2$: input $0,1$ goes to q$3$

$4)$ q$3$: input $0,1$ goes to q$2$

DFA $2$:

$1)$ q$0$: input $1$ goes to q$1,$ input $0$ goes to q$4$

$2)$ q$1$: input $1$ goes to q$2,$ input $0$ goes to q$4$

$3)$ q$2$: input $1$ goes to q$3,$ input $0$ goes to q$4$

$4)$ q$3$: input $0,1$ goes to q$4$

$5)$ q$4$: input $0,1$ goes to q$4$