B'You have been asked to organize a very important art conference. The first step is to choose the dates. The conference must last for a certain number of consecutive days. Each day, one lecturer must perform, and the same lecturer cannot perform more than once. You asked n potential lecturers if they could participate in the conference. Lecturer i indicated that they could perform on any day from l_i to r_i inclusive. A certain segment of days can be chosen as the conference dates if there is a way to assign an available lecturer to each day of the segment, assigning each lecturer to no more than one day. For each k from 1 to n , find how many ways there are to choose a segment of k consecutive days as the conference dates. The first line of input contains one integer n -- the number of potential lecturers ( 1 <= n <= 2 cdot 10^5 ). Each of the next n lines contains two integers l_i and r_i -- the segment of available days for the i th lecturer ( 1 <= l_i <= r_i <= 2 cdot 10^5 ). Print n integers, where the k th number denotes the number of ways to select a segment of k consecutive days as conference dates. In the first testcase, a one-day conference can be organized on any of the days from 1 to 6 . A two-day conference can be organized from day 2 to day 3 , as well as from day 4 to day 5 . In the second testcase, five lecturers can perform only from day 1 to day 3 , so it will not be possible to organize a conference longer than three days. '...