CF1000C.Covered Points Count

You are given $n$ segments on a coordinate line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.

Your task is the following: for every $k \in [1..n]$, calculate the number of points with integer coordinates such that the number of segments that cover these points equals $k$. A segment with endpoints $l_i$ and $r_i$ covers point $x$ if and only if $l_i \le x \le r_i$.

给定坐标轴上的 $n$ 条线段；每条线段的两个端点坐标均为整数。某些线段可能退化为点。线段之间可以相交、嵌套，甚至完全重合。

你的任务是：对每个 $k \in [1..n]$，计算满足“恰好被 $k$ 条线段覆盖”的整数坐标点的个数。其中，端点为 $l_i$ 和 $r_i$ 的线段覆盖点 $x$ 当且仅当 $l_i \le x \le r_i$。

The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of segments.

The next $n$ lines contain segments. The $i$-th line contains a pair of integers $l_i, r_i$ ($0 \le l_i \le r_i \le 10^{18}$) — the endpoints of the $i$-th segment.

输入的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 表示线段的数量。

接下来的 $n$ 行描述这些线段。第 $i$ 行包含一对整数 $l_i, r_i$（$0 \le l_i \le r_i \le 10^{18}$）—— 表示第 $i$ 条线段的两个端点。

Print $n$ space separated integers $cnt_1, cnt_2, \dots, cnt_n$, where $cnt_i$ is equal to the number of points such that the number of segments that cover these points equals to $i$.

输出 $n$ 个以空格分隔的整数 $cnt_1, cnt_2, \dots, cnt_n$，其中 $cnt_i$ 表示被恰好 $i$ 条线段覆盖的点的个数。

The picture describing the first example:

Points with coordinates $[0, 4, 5, 6, 7, 8]$ are covered by one segment, points $[1, 2]$ are covered by two segments and point $[3]$ is covered by three segments.

The picture describing the second example:

Points $[1, 4, 5, 6, 7]$ are covered by one segment, points $[2, 3]$ are covered by two segments and there are no points covered by three segments.

描述第一个示例的图片：

坐标为 $[0, 4, 5, 6, 7, 8]$ 的点被一个线段覆盖，坐标为 $[1, 2]$ 的点被两个线段覆盖，坐标为 $[3]$ 的点被三个线段覆盖。

描述第二个示例的图片：

坐标为 $[1, 4, 5, 6, 7]$ 的点被一个线段覆盖，坐标为 $[2, 3]$ 的点被两个线段覆盖，没有任何点被三个线段覆盖。