CF500E New Year Domino

Celebrating the new year, many people post videos of falling dominoes; Here's a list of them: https://www.youtube.com/results?search\_query=New+Years+Dominos User ainta, who lives in a 2D world, is going to post a video as well. There are $ n $ dominoes on a 2D Cartesian plane. $ i $ -th domino ( $ 1

The first line contains an integer $ n $ ( $ 2

For each plan, print a line containing the minimum cost needed to achieve it. If no cost is needed, print 0.

Consider the example. The dominoes are set like the picture below. Let's take a look at the 4th plan. To make the 6th domino fall by pushing the 2nd domino, the length of the 3rd domino (whose x-coordinate is 4) should be increased by 1, and the 5th domino (whose x-coordinate is 9) should be increased by 1 (other option is to increase 4th domino instead of 5th also by 1). Then, the dominoes will fall like in the picture below. Each cross denotes a touch between two dominoes.