For a word ww$,$ we define even$($w$)$even$($w$)$ to be the word obtained from ww by erasing all symbols it has in odd positions $($assume that the first position has even number $0).$

For example, even$($$)=$even$($$)=$ and even$(1010101)=1111$even$(1010101)=1111.$

Prove that if a language LL is regular, then the language even$($L$)=\{$even$($w$)$w in L$\}$even$($L$)=\{$even$($w$)$w in L$\}$ is also regular.