Consider the system described by the following input$-$output relation:

y$[$n$+1]=$x$[$n$]$x$[$n$+1]$y$[$n$+1]=\backslash$frac$\{$x$[$n$]\}\{$x$[$n$+1]\}$

Determine whether the system is:

i$)$ Linear.

ii$)$ Time$-$invariant.

iii$)$ Causal.

iv$)$ BIBO$-$stable.