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Let G : $\{0,1\}$n $->\{0,1\}2$n be a PRG $($for every n$),$ and let s in $\{0,1\}$n$.$ Prove that the following construction is NOT a secure PRG$.$ Gd$($s$)$: first run G$($s$)=$ x$||$y $($where $|$x$|=|$y$|=$ n$$bits$).$ Then run G$($y$)=$ u$||$v$.$ Output x$||($y $$ u$)||$v$.$ Known fact: if H : $\{0,1\}$n $->\{0,1\}3$n is a PRG$,$ then G$($sL$||$sR$)=$ sL$||$H$($sR$)$ is also a PRG $($where s $=$ sL$||$sR and $|$sL$|=|$sR$|($you can assume n is always even$).$