In the lattice points of the coordinate line there are n radio stations, the i-th of which is described by three integers:
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.
The first line contains two integers n and k (1 ≤ n ≤ 10^{5}, 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} ≤ 10^{9}, 1 ≤ f_{i} ≤ 10^{4}) — 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.
3 2
1 3 10
3 2 5
4 10 8
1
3 3
1 3 10
3 2 5
4 10 8
2
5 1
1 3 2
2 2 4
3 2 1
4 2 1
5 3 3
2
5 1
1 5 2
2 5 4
3 5 1
4 5 1
5 5 3
5
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