CF762E.Radio stations

In the lattice points of the coordinate line there are n radio stations, the i-th of which is described by three integers:

• x__i — the coordinate of the i-th station on the line,
• r__i — the broadcasting range of the i-th station,
• f__i — the broadcasting frequency of the i-th station.

We will say that two radio stations with numbers i and j reach each other, if the broadcasting range of each of them is more or equal to the distance between them. In other words min(r__i, r__j) ≥ |x__i - x__j|.

Let's call a pair of radio stations (i, j) bad if i < j, stations i and j reach each other and they are close in frequency, that is, |f__i - f__j| ≤ k.

Find the number of bad pairs of radio stations.

在坐标轴的格点上有 n 个广播电台，其中第 i 个电台由三个整数描述：

• x__i — 第 i 个电台在坐标轴上的位置（坐标），
• r__i — 第 i 个电台的广播覆盖半径，
• f__i — 第 i 个电台的广播频率。

我们称编号为 i 和 j 的两个广播电台相互可达，当且仅当它们各自的广播半径均不小于二者之间的距离。换言之，满足

$$\min(r_i,\, r_j) \geq |x_i - x_j|.$$

若一对广播电台 (i, j) 满足：i < j，且电台 i 与 j 相互可达，且它们的频率接近（即满足 $|f_i - f_j| \leq k$），则称该对为坏对（bad pair）。

请计算坏对的总数。

The first line contains two integers n and k (1 ≤ n ≤ 105, 0 ≤ k ≤ 10) — the number of radio stations and the maximum difference in the frequencies for the pair of stations that reach each other to be considered bad.

In the next n lines follow the descriptions of radio stations. Each line contains three integers x__i, r__i and f__i (1 ≤ x__i, r__i ≤ 109, 1 ≤ f__i ≤ 104) — the coordinate of the i-th radio station, it's broadcasting range and it's broadcasting frequency. No two radio stations will share a coordinate.

第一行包含两个整数 $n$ 和 $k$（$1 \leq n \leq 10^5$，$0 \leq k \leq 10$）——分别表示广播电台的数量，以及一对能够相互覆盖的电台其频率之差的最大允许值；若超过该值，则称这对电台为“不良对”。

接下来的 $n$ 行描述了各个广播电台。每行包含三个整数 $x_i$、$r_i$ 和 $f_i$（$1 \leq x_i, r_i \leq 10^9$，$1 \leq f_i \leq 10^4$）——分别表示第 $i$ 个广播电台的坐标、广播覆盖半径及其广播频率。任意两个广播电台的坐标均不相同。

Output the number of bad pairs of radio stations.

输出坏的广播电台对的数量。