CF1735B Tea with Tangerines

There are $ n $ pieces of tangerine peel, the $ i $ -th of them has size $ a_i $ . In one step it is possible to divide one piece of size $ x $ into two pieces of positive integer sizes $ y $ and $ z $ so that $ y + z = x $ . You want that for each pair of pieces, their sizes differ strictly less than twice. In other words, there should not be two pieces of size $ x $ and $ y $ , such that $ 2x \le y $ . What is the minimum possible number of steps needed to satisfy the condition?

N/A

N/A

In the first test case, we initially have a piece of size $ 1 $ , so all final pieces must have size $ 1 $ . The total number of steps is: $ 0 + 1 + 2 + 3 + 4 = 10 $ . In the second test case, we have just one piece, so we don't need to do anything, and the answer is $ 0 $ steps. In the third test case, one of the possible cut options is: $ 600,\ 900,\ (600 | 700),\ (1000 | 1000),\ (1000 | 1000 | 550) $ . You can see this option in the picture below. The maximum piece has size $ 1000 $ , and it is less than $ 2 $ times bigger than the minimum piece of size $ 550 $ . $ 4 $ steps are done. We can show that it is the minimum possible number of steps.