In the lattice points of the coordinate line there are *n* radio stations, the *i*-th of which is described by three integers:
 -  *x*<sub class="lower-index">*i*</sub> — the coordinate of the *i*-th station on the line, -  *r*<sub class="lower-index">*i*</sub> — the broadcasting range of the *i*-th station, -  *f*<sub class="lower-index">*i*</sub> — 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*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*j*</sub>) ≥ |*x*<sub class="lower-index">*i*</sub> - *x*<sub class="lower-index">*j*</sub>|.

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, |*f*<sub class="lower-index">*i*</sub> - *f*<sub class="lower-index">*j*</sub>| ≤ *k*.

Find the number of bad pairs of radio stations.
The first line contains two integers *n* and *k* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>, 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*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub> and *f*<sub class="lower-index">*i*</sub> (1 ≤ *x*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>, 1 ≤ *f*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">4</sup>) — 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.
none
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
1 4
6 8 16
0
print("_RANDOM_GUESS_1689177261.6577")# 1689177261.657714