Selection problems in heap: Find the $10$th$$largest element in $150,80,40,30,10,70,110,100,20,90,60,50,120,25,140$using a heap $(20$pts $).$

a$)$Apply the buildHeap algorithm to build a heap. Please draw the final heap $(8$pts$).$

b$)$Perform deleteMin operations to insert the rest of the elements to the root one by one if the new element is larger than the element at the root. Please draw the final heap after each insertion $(10$pts $).$

c$)$At the end of the input, please return the $10$th$$largest element $(2$pts$).$