CF1045G.AI robots

In the last mission, MDCS has successfully shipped $N$ AI robots to Mars. Before they start exploring, system initialization is required so they are arranged in a line. Every robot can be described with three numbers: position ($x_i$), radius of sight ($r_i$) and IQ ($q_i$).

Since they are intelligent robots, some of them will talk if they see each other. Radius of sight is inclusive, so robot can see other all robots in range $[x_i - r_i, x_i + r_i]$. But they don't walk to talk with anybody, but only with robots who have similar IQ. By similar IQ we mean that their absolute difference isn't more than $K$.

Help us and calculate how many pairs of robots are going to talk with each other, so we can timely update their software and avoid any potential quarrel.

在上一次任务中，MDCS 已成功将 $N$ 个 AI 机器人运送至火星。在它们开始探索之前，需进行系统初始化，因此这些机器人被排成一列。每个机器人可用三个数来描述：位置（$x_i$）、可视半径（$r_i$）和智商（$q_i$）。

由于这些是智能机器人，当它们彼此可见时，其中一些会进行交谈。可视半径是包含端点的，因此机器人 $i$ 能看到所有位于区间 $[x_i - r_i, x_i + r_i]$ 内的其他机器人。但它们并不会主动走动去与任意机器人交谈，而只会与智商“相似”的机器人交谈。所谓“相似智商”，是指两个机器人智商的绝对差值不超过 $K$。

请帮助我们计算有多少对机器人将会相互交谈，以便我们能及时更新其软件，避免任何潜在的争执。

The first line contains two integers, numbers $N (1 \leq N \leq 10^5) $ and $K (0 \leq K \leq 20)$.

Next $N$ lines contain three numbers each $x_i, r_i, q_i (0 \leq x_i,r_i,q_i \leq 10^9)$ — position, radius of sight and IQ of every robot respectively.

第一行包含两个整数 $N$（$1 \leq N \leq 10^5$）和 $K$（$0 \leq K \leq 20$）。

接下来的 $N$ 行每行包含三个数 $x_i, r_i, q_i$（$0 \leq x_i,r_i,q_i \leq 10^9$），分别表示每个机器人的位置、视野半径和智商。

Output contains only one number — solution to the problem.

输出仅包含一个数字——问题的解。

The first robot can see the second, but not vice versa. The first robot can't even see the third. The second and the third robot can see each other and their IQs don't differ more than 2 so only one conversation will happen.

第一个机器人能看到第二个机器人，但第二个机器人看不到第一个机器人。第一个机器人甚至看不到第三个机器人。第二个和第三个机器人可以互相看见，且它们的智商相差不超过 2，因此只会发生一次对话。