Letm1, m2,···mnbe distinct numbers on the number line, in the increasing order. Your goalis to color all of them blue. You have magical blue pens with the following property: Whenyou place the pen at co-ordinate x, all the points in the range [x - 5, x + 5] turn blue. Apen can be used only once. Give an algorithm to color all the points using as few pens aspossible. Prove the correctness of the algorithm and derive the runtime.

Write a new lc-3 trap subroutine (i.e. a subroutine that will be invoked via the trap instruction) that will receive a numeric digit entered at the keyboard (i.e. an ascii character), echo it to the screen, and return in r0 the corresponding numeric value: so if the user types the digit '7', the character '7' will appear on the screen, but the value returned in r0 will be b0000 0000 0000 0111 (#7) you may not use any trap calls in your code - you must implement the "polling" code that interrogates the keyboard status and data registers. ; getnum_tsr ; a subroutine for obtaining a numeric value ; given ascii numeric digit input to keyboard. ; the numeric digit is echoed to the console (e.g. '7' = b0000 0000 0011 0111), ; but the value returned in r0 is the actual numeric value ; corresponding to the digit (e.g. b0000 0000 0000 0111 =