Problem: In the lattice points of the coordinate line there are n radio stations, the i-th of which is described by three integers:
- xi — the coordinate of the i-th station on the line,
- ri — the broadcasting range of the i-th station,
- fi — 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(ri, rj) ≥ |xi - xj|.
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, |fi - fj| ≤ k.
Find the number of bad pairs of radio stations.
Input Format: 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 xi, ri and fi (1 ≤ xi, ri ≤ 109, 1 ≤ fi ≤ 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.
Output Format: Output the number of bad pairs of radio stations.