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
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.