Problem: In the last mission, MDCS has successfully shipped N AI robots to Mars. Before they start exploring, system initialization is required so they are arranged in a line. Every robot can be described with three numbers: position (x_i), radius of sight (r_i) and IQ (q_i).

Since they are intelligent robots, some of them will talk if they see each other. Radius of sight is inclusive, so robot can see other all robots in range [x_i - r_i, x_i + r_i]. But they don't walk to talk with anybody, but only with robots who have similar IQ. By similar IQ we mean that their absolute difference isn't more than K. 

Help us and calculate how many pairs of robots are going to talk with each other, so we can timely update their software and avoid any potential quarrel.

Input

The first line contains two integers, numbers N (1 ≤ N ≤ 10^5)  and K (0 ≤ K ≤ 20).

Next N lines contain three numbers each x_i, r_i, q_i (0 ≤ x_i,r_i,q_i ≤ 10^9) — position, radius of sight and IQ of every robot respectively.

Output

Output contains only one number — solution to the problem.

Example

Input

3 2
3 6 1
7 3 10
10 5 8


Output

1

Note

The first robot can see the second, but not vice versa. The first robot can't even see the third. The second and the third robot can see each other and their IQs don't differ more than 2 so only one conversation will happen.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.util.ArrayList;
import java.util.TreeMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Comparator;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskG solver = new TaskG();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskG {
        static int[][] tree;
        static ArrayList<TaskG.pair>[] adj;

        static void build(int i, int n, int nL, int nR) {

            if (nL == nR) {
                tree[i][n] = adj[i].get(nL).i;
                return;
            }

            build(i, 2 * n + 1, nL, (nL + nR) / 2);
            build(i, 2 * n + 2, (nL + nR) / 2 + 1, nR);

            tree[i][n] = tree[i][2 * n + 1] + tree[i][2 * n + 2];
        }

        static int query(int i, int n, int nL, int nR, int l, int r) {

            if (nR < l || r < nL)
                return 0;

            if (l <= nL && nR <= r)
                return tree[i][n];

            return query(i, 2 * n + 1, nL, (nL + nR) / 2, l, r) + query(i, 2 * n + 2, (nL + nR) / 2 + 1, nR, l, r);
        }

        static void update(int i, int n, int nL, int nR, int l, int r) {

            if (nR < l || r < nL)
                return;

            if (l <= nL && nR <= r) {
                tree[i][n]--;
                return;
            }

            update(i, 2 * n + 1, nL, (nL + nR) / 2, l, r);
            update(i, 2 * n + 2, (nL + nR) / 2 + 1, nR, l, r);

            tree[i][n] = tree[i][2 * n + 1] + tree[i][2 * n + 2];
        }

        static int leftIndex(int index, long val) {

            int bs_left = 0, bs_right = adj[index].size() - 1;
            int leftIndex = -1;

            while (bs_left <= bs_right) {

                int mid = (bs_left + bs_right) / 2;

                if (adj[index].get(mid).j >= val) {
                    leftIndex = mid;
                    bs_right = mid - 1;
                } else
                    bs_left = mid + 1;
            }

            return leftIndex;
        }

        static int rightIndex(int index, long val) {

            int bs_left = 0, bs_right = adj[index].size() - 1;
            int rightIndex = -1;

            while (bs_left <= bs_right) {

                int mid = (bs_left + bs_right) / 2;

                if (adj[index].get(mid).j <= val) {
                    rightIndex = mid;
                    bs_left = mid + 1;
                } else
                    bs_right = mid - 1;
            }

            return rightIndex;
        }

        public void solve(int testNumber, InputReader s, PrintWriter w) {

            int n = s.nextInt(), k = s.nextInt();

            TreeSet<Long> ts = new TreeSet<Long>();

            long[] x = new long[n];
            long[] r = new long[n];
            long[] q = new long[n];

            for (int i = 0; i < n; i++) {
                x[i] = s.nextLong();
                r[i] = s.nextLong();
                q[i] = s.nextLong();
                ts.add(q[i]);
            }

            int m = ts.size();

            long[] val = new long[m];

            int c = 0;

            for (long i : ts)
                val[c++] = i;

            HashMap<Long, Integer> map = new HashMap<Long, Integer>();

            for (int i = 0; i < m; i++)
                map.put(val[i], i);

            TreeMap<Long, Integer>[] tm = new TreeMap[m];

            for (int i = 0; i < m; i++)
                tm[i] = new TreeMap<Long, Integer>();

            for (int i = 0; i < n; i++) {

                int index = map.get(q[i]);

                if (tm[index].get(x[i]) == null)
                    tm[index].put(x[i], 1);
                else
                    tm[index].put(x[i], tm[index].get(x[i]) + 1);
            }

            adj = new ArrayList[m];

            for (int i = 0; i < m; i++) {

                adj[i] = new ArrayList<TaskG.pair>();

                for (Map.Entry<Long, Integer> e : tm[i].entrySet())
                    adj[i].add(new TaskG.pair(e.getValue(), e.getKey()));
            }

            tree = new int[m][];

            for (int i = 0; i < m; i++) {

                int temp = (int) Math.pow(2, (int) Math.ceil(Math.log(adj[i].size()) / Math.log(2)) + 1);
                tree[i] = new int[temp];

                build(i, 0, 0, adj[i].size() - 1);
            }

            ArrayList<TaskG.pair> list = new ArrayList<TaskG.pair>();

            for (int i = 0; i < n; i++)
                list.add(new TaskG.pair(i, r[i]));

            Collections.sort(list, new TaskG.comp());

            long res = 0;

            for (int i = 0; i < list.size(); i++) {

                int personIndex = list.get(i).i;

                long iq = q[personIndex];
                int index = map.get(iq);

                int pos = leftIndex(index, x[personIndex]);
                update(index, 0, 0, adj[index].size() - 1, pos, pos);

                for (int j = index; j < m; j++) {

                    if (val[j] > iq + k)
                        break;

                    int leftIndex = leftIndex(j, x[personIndex] - r[personIndex]);
                    int rightIndex = rightIndex(j, x[personIndex] + r[personIndex]);

                    if (leftIndex != -1 && rightIndex != -1 && leftIndex <= rightIndex)
                        res += query(j, 0, 0, adj[j].size() - 1, leftIndex, rightIndex);
                }

                for (int j = index - 1; j >= 0; j--) {

                    if (val[j] < iq - k)
                        break;

                    int leftIndex = leftIndex(j, x[personIndex] - r[personIndex]);
                    int rightIndex = rightIndex(j, x[personIndex] + r[personIndex]);

                    if (leftIndex != -1 && rightIndex != -1 && leftIndex <= rightIndex)
                        res += query(j, 0, 0, adj[j].size() - 1, leftIndex, rightIndex);
                }

            }

            w.println(res);
        }

        static class pair {
            int i;
            long j;

            pair(int i, long j) {
                this.i = i;
                this.j = j;
            }

        }

        static class comp implements Comparator<TaskG.pair> {
            public int compare(TaskG.pair x, TaskG.pair y) {

                if (x.j < y.j)
                    return -1;

                if (x.j > y.j)
                    return 1;

                return 0;
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}