Problem: Polycarpus has a hobby — he develops an unusual social network. His work is almost completed, and there is only one more module to implement — the module which determines friends. Oh yes, in this social network one won't have to add friends manually! Pairs of friends are deduced in the following way. Let's assume that user A sent user B a message at time t1, and user B sent user A a message at time t2. If 0 < t2 - t1 ≤ d, then user B's message was an answer to user A's one. Users A and B are considered to be friends if A answered at least one B's message or B answered at least one A's message.

You are given the log of messages in chronological order and a number d. Find all pairs of users who will be considered to be friends.

Input

The first line of the input contains two integers n and d (1 ≤ n, d ≤ 1000). The next n lines contain the messages log. The i-th line contains one line of the log formatted as "Ai Bi ti" (without the quotes), which means that user Ai sent a message to user Bi at time ti (1 ≤ i ≤ n). Ai and Bi are non-empty strings at most 20 characters long, consisting of lowercase letters ('a' ... 'z'), and ti is an integer (0 ≤ ti ≤ 10000). It is guaranteed that the lines are given in non-decreasing order of ti's and that no user sent a message to himself. The elements in the lines are separated by single spaces.

Output

In the first line print integer k — the number of pairs of friends. In the next k lines print pairs of friends as "Ai Bi" (without the quotes). You can print users in pairs and the pairs themselves in any order. Each pair must be printed exactly once.

Examples

Input

4 1
vasya petya 1
petya vasya 2
anya ivan 2
ivan anya 4


Output

1
petya vasya


Input

1 1000
a b 0


Output

0

Note

In the first sample test case Vasya and Petya are friends because their messages' sending times are one second apart. Anya and Ivan are not, because their messages' sending times differ by more than one second.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class TaskA implements Runnable {
    private BufferedReader reader;
    private PrintWriter writer;
    private StringTokenizer tokenizer;

    public static void main(String[] args) {
        new Thread(new TaskA()).start();
    }

    private String next() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }

        return tokenizer.nextToken();
    }

    private int nextInt() throws Exception {
        return Integer.parseInt(next());
    }

    @Override
    public void run() {
        try {
            reader = new BufferedReader(new InputStreamReader(System.in));
            writer = new PrintWriter(System.out);

            solve();

            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    private void solve() throws Exception {
        int n = nextInt();
        int d = nextInt();

        Map<Pair, List<Integer>> pairAppearanceTime = new HashMap<Pair, List<Integer>>();
        Set<Pair> friends = new TreeSet<Pair>(new Comparator<Pair>() {
            @Override
            public int compare(Pair o1, Pair o2) {
                return o1.compareIgnoreOrder(o2);
            }
        });

        for (int i = 0; i < n; i++) {
            String first = next();
            String second = next();

            Pair reversePair = new Pair(second, first);
            int time = nextInt();

            if (pairAppearanceTime.containsKey(reversePair)) {
                List<Integer> times = pairAppearanceTime.get(reversePair);

                for (int j = times.size() - 1; j >= 0; j--) {
                    int dif = time - times.get(j);
                    if (dif > d) {
                        break;
                    }
                    if (dif > 0) {
                        friends.add(reversePair);
                        break;
                    }
                }
            }

            Pair pair = new Pair(first, second);
            if (!pairAppearanceTime.containsKey(pair)) {
                pairAppearanceTime.put(pair, new ArrayList<Integer>());
            }
            pairAppearanceTime.get(pair).add(time);
        }

        writer.println(friends.size());
        for (Pair friend : friends) {
            writer.println(friend);
        }
    }

    private static class Pair {
        private String first;
        private String second;

        private String sMin;
        private String sMax;

        private Pair(String first, String second) {
            this.first = first;
            this.second = second;

            if (first.compareTo(second) <= 0) {
                sMin = first;
                sMax = second;
            } else {
                sMin = second;
                sMax = first;
            }
        }

        @SuppressWarnings("RedundantIfStatement")
        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Pair pair = (Pair) o;

            if (!first.equals(pair.first)) return false;
            if (!second.equals(pair.second)) return false;

            return true;
        }

        public int compareIgnoreOrder(Object obj) {
            Pair o = (Pair) obj;

            int cmp1 = sMin.compareTo(o.sMin);
            if (cmp1 != 0) {
                return cmp1;
            }

            return sMax.compareTo(o.sMax);
        }

        @Override
        public int hashCode() {
            int result = first.hashCode();
            result = 31 * result + second.hashCode();
            return result;
        }

        @Override
        public String toString() {
            return first + " " + second;
        }
    }
}