Problem: There are N cards placed on a grid with H rows and W columns of squares.

The i-th card has an integer A_i written on it, and it is placed on the square at the R_i-th row from the top and the C_i-th column from the left.

Multiple cards may be placed on the same square.

You will first pick up at most one card from each row.

Then, you will pick up at most one card from each column.

Find the maximum possible sum of the integers written on the picked cards.

Constraints

* All values are integers.
* 1 \leq N \leq 10^5
* 1 \leq H, W \leq 10^5
* 1 \leq A_i \leq 10^5
* 1 \leq R_i \leq H
* 1 \leq C_i \leq W

Input

Input is given from Standard Input in the following format:


N H W
R_1 C_1 A_1
R_2 C_2 A_2
\vdots
R_N C_N A_N


Output

Print the maximum possible sum of the integers written on the picked cards.

Examples

Input

6 2 2
2 2 2
1 1 8
1 1 5
1 2 9
1 2 7
2 1 4


Output

28


Input

13 5 6
1 3 35902
4 6 19698
4 6 73389
3 6 3031
3 1 4771
1 4 4784
2 1 36357
2 1 24830
5 6 50219
4 6 22645
1 2 30739
1 4 68417
1 5 78537


Output

430590


Input

1 100000 100000
1 1 1


Output

1

Solution (in JAVA):

Solution:

import java.util.Arrays;

class DisjointSet {
  public int[] upper; // minus:num_element(root) plus:root(normal)
  public int[] w;
  public int[] e;

  public DisjointSet(int n) {
    upper = new int[n];
    w = new int[n];
    e = new int[n];
    Arrays.fill(w, 1);
    Arrays.fill(upper, -1);
  }

  public DisjointSet(DisjointSet ds) {
    this.upper = Arrays.copyOf(ds.upper, ds.upper.length);
  }

  public int root(int x) {
    return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
  }

  public boolean equiv(int x, int y) {
    return root(x) == root(y);
  }

  public boolean union(int x, int y) {
    x = root(x);
    y = root(y);
    if (x != y) {
      if (upper[y] < upper[x]) {
        int d = x;
        x = y;
        y = d;
      }
      w[x] += w[y];
      e[x] += e[y];
      upper[x] += upper[y];
      upper[y] = x;
    }
    e[x]++;
    return x == y;
  }

}


public class Main {
  private static void solve() {
    int n = ni();
    int h = ni();
    int w = ni();
    int[][] cards = ntable(n, 3);

    Arrays.sort(cards, (o1, o2) -> o2[2] - o1[2]);

    DisjointSet ds = new DisjointSet(h + w);

    long ret = 0;
    for (int[] e : cards) {
      int u = ds.root(e[0] - 1);
      int v = ds.root(e[1] - 1 + h);

      if (ds.e[u] + ds.e[v] + 1 <= ds.w[u] + ds.w[v]) {
        ds.union(u, v);
        ret += e[2];
      }
    }

    System.out.println(ret);
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}