Q$3(10$ points$)$ Consider a $1\backslash$times n strip of cells containing white, grey, and black stones with the following rules: $($i$)$ Every cell contains exactly one stone. $($ii$)$ There is at least one black stone on the strip. $($iii$)$ A grey stone cannot be adjacent to a black stone. $($iv$)$ All cells to the left of a white stone are occupied by white stones. For each i$=1,2,...,$n $,$ let wi $,$ gi $,$ bi be boolean variables. We interpret wi$=1$ to mean there is a white stone on cell i and wi$=0$ to mean there is not a white stone on cell i $.$ Similarly for gi $($grey$)$ and bi $($black$).$ Write down a boolean formula F such that for any assignment of values $(0$ or $1)$ to the variables, F evaluates to true if and only if the rules above are respected. You may use the following notations, similar to the sigma notation used for sums: $$i$=1$nxi$=$x$1$x$2...$xn $$i$=1$nxi$=$x$1$x$2...$xn