Chef and Rods

Chef placed N rods on a straight line. The i-th rod is located at position xi and has length li. There are no two rods located at the same position. Chef can push rods to make them fall in any direction(left or right). A rod can touch its neighbors while falling and make them fall too in the similar direction $((x-h)$ to $(x+h))$.Chef wants to minimize the number of rods needed to push to make all