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time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

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 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.

Output

Examples
Input
3 21 3 103 2 54 10 8
Output
1
Input
3 31 3 103 2 54 10 8
Output
2
Input
5 11 3 22 2 43 2 14 2 15 3 3
Output
2
Input
5 11 5 22 5 43 5 14 5 15 5 3
Output
5