$(4$ points$)$ Let $=\{u,d,l,r\}$ be commands for a robot pen. Here is what the robot does for each command:

For $u,$ it draws a $1$ in line segment going up in the page.

For d$,$ it draws a $1$ in line segment going down in the page.

For $1,$ it draws a $1$ in line segment going left in the page.

For $r,$ it draws a $1$ in line segment going right in the page.

For example, when executing uuldr, the robot draws the following picture $($starting from the star$)$:

Let

RECT$=\{win{}^{**}|w$ when the robot executes $w,it$ draws a rectangle $\}.$

Show that RECT is not regular.