TR-MO 1999 Problem 6

We wish to find the sum of $40$ given numbers utilizing $40$ processors. Initially, we have the number $0$ on the screen of each processor. Each processor adds the number on its screen with a number entered directly (only the given numbers could be entered directly to the processors) or transferred from another processor in a unit time. Whenever a number is transferred from a processor to another, the former processor resets. Find the least time needed to find the desired sum.