Problem $2.$ Let $(Ge{n}_0,Sig{n}_0,Ve{r}_0),(Ge{n}_1,Sig{n}_1,Ve{r}_1)$ be two digital signature schemes. Sup$-$

pose you are guaranteed that both are correct, but only one of the schemes is UF$-$CMA$-$secure$,$ and

you don't know which is the secure one.

From these two schemes, construct a new "combined" signature scheme $($Gen$,$ Sign, Ver$)$ that is

provably UF$-$CMA, provided at least one of the two schemes is UF$-$CMA. Give a clear description of

the scheme, and theorem statement $($that you must prove$)$ that gives the security of your constructed

scheme.

I am not expecting a chatgpt response copy paste. I need technicaly sound answer. Please only use the notations givene in the question.