Let

f$($x$)=\{|$x$|$x$2$a$2$x$$aif$$x$<1,$if$$x$>1.$f$($x$)=\{|$x$|$if$$x$<1,$x$2$a$2$x$$aif$$x$>1.$

If limx$1$f$($x$)$limx$1$f$($x$)$ exists, what must be the value of aa$?$

a$=$