For a string a$1$a$2$ an define the operation shif t as

shif t $($a$1$a$2$ an$)=$ a$2$ ana$1.$

From this, we can define the operation on a language as

shif t $($L$)=\{$v : v $=$ shif t $($w$)$ for some w in L$\}.$

Show that regularity is preserved under the shif t operation