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.io.*;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.Function;

public class Main {

    static int N, H, W;
    static int[][] C;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        H = sc.nextInt();
        W = sc.nextInt();

        C = new int[N][3];
        for (int i = 0; i < N; i++) {
            C[i][0] = sc.nextInt()-1;
            C[i][1] = sc.nextInt()-1;
            C[i][2] = sc.nextInt();
        }

        System.out.println(solve());
    }

    static long solve() {
        // 行と列を頂点、カードを辺を見なす
        // 関数グラフとみなせる最大のものが答え
        //   関数グラフ -> 連結成分に対して閉路一つまではok
        // クラスカルっぽい感じで辺を選んでいけばよい

        UnionFind uf = new UnionFind(H+W);
        boolean[] hasCycle = new boolean[H+W];
        Arrays.sort(C, Comparator.comparingInt(c -> -c[2]));

        long ans = 0;
        for (int i = 0; i < N; i++) {
            int h = C[i][0];
            int w = C[i][1] + H;
            int a = C[i][2];

            if( uf.isSame(h, w) ) {
                int g = uf.root(h);
                if( hasCycle[g] ) {
                    // すでにcycleがあるのでダメ

                } else {
                    ans += a;
                    hasCycle[g] = true;
                }

            } else {
                int gh = uf.root(h);
                int gw = uf.root(w);
                if( hasCycle[gh] && hasCycle[gw] ) {
                    // 両方cycleなのでダメ

                } else if( !hasCycle[gh] && !hasCycle[gw] ) {
                    // どっちもcycle持たないのでつなげるだけ
                    uf.unite(h, w);
                    ans += a;

                } else {
                    // 片方が持ってるのでつなげた後もcycleあり
                    uf.unite(h, w);
                    ans += a;
                    hasCycle[uf.root(h)] = true;
                }
            }
        }
        return ans;
    }

    static class UnionFind {

        private final int[] parent;
        private final int[] count;

        public UnionFind(int n) {
            parent = new int[n];
            count = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                count[i] = 1;
            }
        }

        public int root(int i) {
            if (parent[i] == i) {
                return i;
            } else {
                return parent[i] = root(parent[i]);
            }
        }

        public int unite(int i, int j) {
            int ri = root(i);
            int rj = root(j);
            if (ri == rj) return ri;


            int big = count[ri] < count[rj] ? rj : ri;
            int small = big == ri ? rj : ri;
            parent[small] = big;
            count[big] += count[small];
            return big;
        }

        public int count(int a) {
            return count[root(a)];
        }

        public boolean isSame(int a, int b) {
            return root(a) == root(b);
        }
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}