Radio stations

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.

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 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

Output the number of bad pairs of radio stations.

Examples

input

3 2
1 3 10
3 2 5
4 10 8

output

1

input

3 3
1 3 10
3 2 5
4 10 8

output

2

input

5 1
1 3 2
2 2 4
3 2 1
4 2 1
5 3 3

output

2

input

5 1
1 5 2
2 5 4
3 5 1
4 5 1
5 5 3

output

5

Solution:

#include <bits/stdc++.h>

using namespace std;

mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());

class node {
public:
int id;
node* l;
node* r;
node* p;
bool rev;
int sz;
// declare extra variables:
int P;

node(int _id) {
id = _id;
l = r = p = NULL;
rev = false;
sz = 1;
// init extra variables:
P = rng();
}

void unsafe_reverse() {
rev ^= 1;
swap(l, r);
pull();
}

// apply changes:
void unsafe_apply() {

}

void push() {
if (rev) {
if (l != NULL) {
l->unsafe_reverse();
}
if (r != NULL) {
r->unsafe_reverse();
}
rev = 0;
}
// now push everything else:

}

void pull() {
sz = 1;
// now init from self:

if (l != NULL) {
l->p = this;
sz += l->sz;
// now pull from l:

}
if (r != NULL) {
r->p = this;
sz += r->sz;
// now pull from r:

}
}
};

void debug_node(node* v, string pref = "") {
#ifdef LOCAL
if (v != NULL) {
debug_node(v->r, pref + " ");
cerr << pref << "-" << " " << v->id << '\n';
      debug_node(v->l, pref + " ");
} else {
cerr << pref << "-" << " " << "NULL" << '\n';
    }
  #endif
}

namespace treap {
  pair<node*,int> find(node* v, const function<int(node*)> &go_to) {
// go_to returns: 0 -- found; -1 -- go left; 1 -- go right
// find returns the last vertex on the descent and its go_to
if (v == NULL) {
return {NULL, 0};
}
int dir;
while (true) {
v->push();
dir = go_to(v);
if (dir == 0) {
break;
}
node* u = (dir == -1 ? v->l : v->r);
if (u == NULL) {
break;
}
v = u;
}
return {v, dir};
}

node* get_leftmost(node* v) {
return find(v, [&](node*) { return -1; }).first;
}

node* get_rightmost(node* v) {
return find(v, [&](node*) { return 1; }).first;
}

node* get_kth(node* v, int k) { // 0-indexed
pair<node*,int> p = find(v, [&](node* u) {
if (u->l != NULL) {
if (u->l->sz > k) {
return -1;
}
k -= u->l->sz;
}
if (k == 0) {
return 0;
}
k--;
return 1;
});
return (p.second == 0 ? p.first : NULL);
}

int get_position(node* v) { // 0-indexed
int k = (v->l != NULL ? v->l->sz : 0);
while (v->p != NULL) {
if (v == v->p->r) {
k++;
if (v->p->l != NULL) {
k += v->p->l->sz;
}
}
v = v->p;
}
return k;
}

node* get_bst_root(node* v) {
while (v->p != NULL) {
v = v->p;
}
return v;
}

pair<node*,node*> split(node* v, const function<bool(node*)> &is_right) {
if (v == NULL) {
return {NULL, NULL};
}
v->push();
if (is_right(v)) {
pair<node*,node*> p = split(v->l, is_right);
if (p.first != NULL) {
p.first->p = NULL;
}
v->l = p.second;
v->pull();
return {p.first, v};
} else {
pair<node*,node*> p = split(v->r, is_right);
v->r = p.first;
if (p.second != NULL) {
p.second->p = NULL;
}
v->pull();
return {v, p.second};
}
}

pair<node*,node*> split_leftmost_k(node* v, int k) {
return split(v, [&](node* u) {
int left_and_me = (u->l != NULL ? u->l->sz : 0) + 1;
if (k >= left_and_me) {
k -= left_and_me;
return false;
}
return true;
});
}

node* merge(node* v, node* u) {
if (v == NULL) {
return u;
}
if (u == NULL) {
return v;
}
if (v->P > u->P) {
//    if (rng() % (v->sz + u->sz) < (unsigned int) v->sz) {
v->push();
v->r = merge(v->r, u);
v->pull();
return v;
} else {
u->push();
u->l = merge(v, u->l);
u->pull();
return u;
}
}

node* add(node* r, node* v, const function<bool(node*)> &go_left) {
pair<node*,node*> p = split(r, go_left);
return merge(p.first, merge(v, p.second));
}

node* remove(node* v) { // returns the new root
v->push();
node* x = v->l;
node* y = v->r;
node* p = v->p;
v->l = v->r = v->p = NULL;
v->push();
v->pull(); // now v might be reusable...
node* z = merge(x, y);
if (p == NULL) {
if (z != NULL) {
z->p = NULL;
}
return z;
}
if (p->l == v) {
p->l = z;
}
if (p->r == v) {
p->r = z;
}
while (true) {
p->push();
p->pull();
if (p->p == NULL) {
break;
}
p = p->p;
}
return p;
}

node* next(node* v) {
if (v->r == NULL) {
while (v->p != NULL && v->p->r == v) {
v = v->p;
}
return v->p;
}
v->push();
v = v->r;
while (v->l != NULL) {
v->push();
v = v->l;
}
return v;
}

node* prev(node* v) {
if (v->l == NULL) {
while (v->p != NULL && v->p->l == v) {
v = v->p;
}
return v->p;
}
v->push();
v = v->l;
while (v->r != NULL) {
v->push();
v = v->r;
}
return v;
}

int get_size(node* v) {
return (v != NULL ? v->sz : 0);
}

template<typename... T>
void apply(node* v, T... args) {
v->unsafe_apply(args...);
}

void reverse(node* v) {
v->unsafe_reverse();
}
}

using namespace treap;

int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int n, k;
cin >> n >> k;
vector<int> x(n), r(n), f(n);
for (int i = 0; i < n; i++) {
    cin >> x[i] >> r[i] >> f[i];
}
vector<int> order(n);
iota(order.begin(), order.end(), 0);
sort(order.begin(), order.end(), [&](int i, int j) { return r[i] > r[j]; });
const int MAX = 10010;
vector<node*> nodes(MAX, NULL);
long long ans = 0;
for (int i : order) {
for (int j = max(0, f[i] - k); j <= min(MAX - 1, f[i] + k); j++) {
      pair<node*,node*> p = split(nodes[j], [&](node* v) { return x[i] + r[i] < v->id; });
pair<node*,node*> q = split(p.first, [&](node* v) { return x[i] - r[i] <= v->id; });
ans += get_size(q.second);
nodes[j] = merge(q.first, merge(q.second, p.second));
}
nodes[f[i]] = add(nodes[f[i]], new node(x[i]), [&](node* v) { return x[i] < v->id; });
}
cout << ans << '\n';
  return 0;
}