Given n rectangular boxes, each with the same height but varying widths along the x$-$axis. These boxes are placed on a table along the z$-$axis, such that they do not overlap or touch each other. From the negative z$-$axis, a photograph is taken of these boxes from a viewpoint facing the x$-$y plane. Each box b$$is represented by a triplet$($l$,$r$,$z$),$where:

$-$l$$is the left x$-$coordinate of box b$.$

$-$r$$is the right x$-$coordinate of box b$.$

$-$z$$is the z$-$coordinate of the center of box b$.$

Code and explain a divide$-$and$-$conquer algorithm that identifies all boxes that are visible$($either fully or partially$)$in the photograph, excluding those completely obscured by others. Provide the recurrence relation for your algorithm and determine its time complexity, ensuring the algorithm is more efficient than$($n$^2).$The provided code should produce correct output on sample input$"\{$b$1=(2,4,3),$b$2=(3,6,1),$b$3=(3,5,5),$b$4=(5,8,2),$b$5=(6,10,5),$b$6=(7,10,1),$b$7=(12,14,1)\}.$while correct Output is:$\{$b$1,$b$2,$b$4,$b$6,$b$7\}""$Take the screenshot of the output after running the code"