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) \ge |xi-xj|.

Let's call a pair of radio stations (i,j) bad if i \lt j, stations i and j reach each other and they are close in frequency, that is, |fi-fj| \le k.

Find the number of bad pairs of radio stations.

The first line contains two integers n and k (1 \le n \le 105, 0 \le k \le 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 \le xi,ri \le 109, 1 \le fi \le 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 the number of bad pairs of radio stations.