$($Closure under repetition$)$ Let $$ be a finite alphabet. For a string $w=w_{1}dots{w}_n,$ where

each $w_{i}in,$ define Rep$(w)=w_1{w}_1{w}_2{w}_{2}dots{w}_n{w}_n.$ That is$,$ Rep$(w)$ is the string obtained by

repeating each character in $w$ one additional time. Given a language Lsube${}^{**},$ define the language

Rep$(L)=\{Rep(w)|winL\}.$ Show that the class of regular languages is closed under Rep.