Problem:
Score : 800 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

28

The sum of the integers written on the picked cards will be 28, the maximum value possible, if you pick up cards as follows:

Pick up the fourth card from the first row.

Pick up the sixth card from the second row.

Pick up the second card from the first column.

Pick up the fifth card from the second column.

Sample Input 2

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

Sample Output 2

430590

Sample Input 3

1 100000 100000
1 1 1

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Linq.Expressions;
using System.IO;
using System.Threading;
using System.Text;
using System.Diagnostics;

using static util;
using P = pair<int, int>;

using Binary = System.Func<System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.ParameterExpression,
                           System.Linq.Expressions.BinaryExpression>;
using Unary = System.Func<System.Linq.Expressions.ParameterExpression,
                          System.Linq.Expressions.UnaryExpression>;

class Program {
    static StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
    static Scan sc = new Scan();
    const int M = 1000000007;
    const int M2 = 998244353;
    const long LM = 1L << 60;
    const double eps = 1e-11;
    static void DBG(string a) => Console.WriteLine(a);
    static void DBG<T>(IEnumerable<T> a) => DBG(string.Join(" ", a));
    static void DBG(params object[] a) => DBG(string.Join(" ", a));
    static void Prt(string a) => sw.WriteLine(a);
    static void Prt<T>(IEnumerable<T> a) => Prt(string.Join(" ", a));
    static void Prt(params object[] a) => Prt(string.Join(" ", a));

    static void Main(string[] args)
    {
        var solver = new Solver();
        // var t = new Thread(solver.solve, 1 << 26); // 64 MB
		// t.Start();
		// t.Join();
        solver.solve();
        sw.Flush();
    }


    class Solver {
        public void solve() {
            int n, h, w;
            sc.Multi(out n, out h, out w);
            var p = new pair<P, int>[n];
            var ph = new List<P>[h];
            var pw = new List<P>[w];
            for (int i = 0; i < h; i++)
            {
                ph[i] = new List<P>();
            }
            for (int i = 0; i < w; i++)
            {
                pw[i] = new List<P>();
            }
            var uf = new UnionFind(h + w);
            for (int i = 0; i < n; i++)
            {
                int r, c, a;
                sc.Multi(out r, out c, out a);
                --r;
                --c;
                p[i] = make_pair(new P(r, c), a);
                ph[r].Add(new P(a, i));
                pw[c].Add(new P(a, i));
            }
            var used = new int[n];
            long ans = 0;
            for (int i = 0; i < h; i++)
            {
                if (ph[i].Count == 0) continue;
                ph[i].Sort();
                ph[i].Reverse();
                if (used[ph[i][0].v2] == 0)
                    ans += ph[i][0].v1;
                ++used[ph[i][0].v2];
            }
            for (int i = 0; i < w; i++)
            {
                if (pw[i].Count == 0) continue;
                pw[i].Sort();
                pw[i].Reverse();
                if (used[pw[i][0].v2] == 0)
                    ans += pw[i][0].v1;
                ++used[pw[i][0].v2];
            }
            var cnt = new int[h + w];
            var lis = new List<P>[h + w];
            for (int i = 0; i < h + w; i++)
            {
                lis[i] = new List<P>();
            }
            for (int i = 0; i < n; i++)
            {
                if (used[i] > 0) {
                    uf.unite(p[i].v1.v1, h + p[i].v1.v2);
                }
            }
            for (int i = 0; i < n; i++)
            {
                if (used[i] == 0)
                    lis[uf.getpar(p[i].v1.v1)].Add(new P(p[i].v2, i));
                else {
                    cnt[uf.getpar(p[i].v1.v1)] += used[i] - 1;
                }
            }
            for (int i = 0; i < h + w; i++)
            {
                lis[i].Sort();
                lis[i].Reverse();
                foreach (var item in lis[i])
                {
                    if (cnt[i] > 0) {
                        --cnt[i];
                        ans += item.v1;
                    }
                }
            }
            Prt(ans);
        } // end Solver.solve

    }
}

class pair<T, U> : IComparable<pair<T, U>> {
    public T v1;
    public U v2;
    public pair() : this(default(T), default(U)) {}
    public pair(T v1, U v2) { this.v1 = v1; this.v2 = v2; }
    public int CompareTo(pair<T, U> a) {
        int c = Comparer<T>.Default.Compare(v1, a.v1);
        return c != 0 ? c : Comparer<U>.Default.Compare(v2, a.v2);
    }
    public override string ToString() => v1 + " " + v2;
    public void Deconstruct(out T a, out U b) { a = v1; b = v2; }
    public static bool operator>(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) > 0;
    public static bool operator<(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) < 0;
    public static bool operator>=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) >= 0;
    public static bool operator<=(pair<T, U> a, pair<T, U> b) => a.CompareTo(b) <= 0;
}
static class util {
    public static pair<T, U> make_pair<T, U>(T v1, U v2) => new pair<T, U>(v1, v2);
    public static T sq<T>(T a) => Operator<T>.Multiply(a, a);
    public static T Max<T>(params T[] a) => a.Max();
    public static T Min<T>(params T[] a) => a.Min();
    public static bool inside(int i, int j, int h, int w) => i >= 0 && i < h && j >= 0 && j < w;
    static readonly int[] dd = { 0, 1, 0, -1 };
    static readonly string dstring = "RDLU";
    public static P[] adjacents(this P p) => adjacents(p.v1, p.v2);
    public static P[] adjacents(this P p, int h, int w) => adjacents(p.v1, p.v2, h, w);
    public static pair<P, char>[] adjacents_with_str(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new pair<P, char>(new P(i + dd[k], j + dd[k ^ 1]), dstring[k])).ToArray();
    public static pair<P, char>[] adjacents_with_str(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new pair<P, char>(new P(i + dd[k], j + dd[k ^ 1]), dstring[k]))
                                         .Where(p => inside(p.v1.v1, p.v1.v2, h, w)).ToArray();
    public static P[] adjacents(int i, int j)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).ToArray();
    public static P[] adjacents(int i, int j, int h, int w)
        => Enumerable.Range(0, dd.Length).Select(k => new P(i + dd[k], j + dd[k ^ 1])).Where(p => inside(p.v1, p.v2, h, w)).ToArray();
    public static void Assert(bool cond) { if (!cond) throw new Exception(); }
    public static Dictionary<T, int> compress<T>(this IEnumerable<T> a)
        => a.Distinct().OrderBy(v => v).Select((v, i) => new { v, i }).ToDictionary(p => p.v, p => p.i);
    public static Dictionary<T, int> compress<T>(params IEnumerable<T>[] a) => compress(a.Aggregate(Enumerable.Union));
    public static void swap<T>(ref T a, ref T b) where T : struct { var t = a; a = b; b = t; }
    public static void swap<T>(this IList<T> a, int i, int j) where T : struct { var t = a[i]; a[i] = a[j]; a[j] = t; }
    public static T[] copy<T>(this IList<T> a) {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
static class Operator<T> {
    static readonly ParameterExpression x = Expression.Parameter(typeof(T), "x");
    static readonly ParameterExpression y = Expression.Parameter(typeof(T), "y");
    public static readonly Func<T, T, T> Add = Lambda(Expression.Add);
    public static readonly Func<T, T, T> Subtract = Lambda(Expression.Subtract);
    public static readonly Func<T, T, T> Multiply = Lambda(Expression.Multiply);
    public static readonly Func<T, T, T> Divide = Lambda(Expression.Divide);
    public static readonly Func<T, T> Plus = Lambda(Expression.UnaryPlus);
    public static readonly Func<T, T> Negate = Lambda(Expression.Negate);
    public static Func<T, T, T> Lambda(Binary op) => Expression.Lambda<Func<T, T, T>>(op(x, y), x, y).Compile();
    public static Func<T, T> Lambda(Unary op) => Expression.Lambda<Func<T, T>>(op(x), x).Compile();
}

class Scan {
    StreamReader sr;
    public Scan() { sr = new StreamReader(Console.OpenStandardInput()); }
    public Scan(string path) { sr = new StreamReader(path); }
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public string Str => sr.ReadLine().Trim();
    public pair<T, U> Pair<T, U>() {
        T a; U b;
        Multi(out a, out b);
        return new pair<T, U>(a, b);
    }
    public P P => Pair<int, int>();
    public int[] IntArr => StrArr.Select(int.Parse).ToArray();
    public long[] LongArr => StrArr.Select(long.Parse).ToArray();
    public double[] DoubleArr => StrArr.Select(double.Parse).ToArray();
    public string[] StrArr => Str.Split(new[]{' '}, StringSplitOptions.RemoveEmptyEntries);
    bool eq<T, U>() => typeof(T).Equals(typeof(U));
    T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
    T cv<T>(string s) => eq<T, int>()    ? ct<T, int>(int.Parse(s))
                       : eq<T, long>()   ? ct<T, long>(long.Parse(s))
                       : eq<T, double>() ? ct<T, double>(double.Parse(s))
                       : eq<T, char>()   ? ct<T, char>(s[0])
                                         : ct<T, string>(s);
    public void Multi<T>(out T a) => a = cv<T>(Str);
    public void Multi<T, U>(out T a, out U b)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); }
    public void Multi<T, U, V>(out T a, out U b, out V c)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); }
    public void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); }
    public void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
    { var ar = StrArr; a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); }
}
class UnionFind {
    int num;
    int[] par, sz, rank;
    public UnionFind(int n) {
        num = n; par = new int[n]; sz = new int[n]; rank = new int[n];
        for (int i = 0; i < n; ++i) { par[i] = i; sz[i] = 1; rank[i] = 0; }
    }
    int find(int x) => par[x] == x ? x : (par[x] = find(par[x]));
    public bool same(int x, int y) => find(x) == find(y);
    public int unionsize(int x) => sz[find(x)];
    public int unioncount => num;
    public bool unite(int x, int y) {
        x = find(x); y = find(y);
        if (x == y) return false;
        --num;
        if (rank[x] < rank[y]) {
            par[x] = y;
            sz[y] += sz[x];
        }
        else {
            par[y] = x;
            sz[x] += sz[y];
            if (rank[x] == rank[y]) ++rank[x];
        }
        return true;
    }
    public bool ispar(int x) => x == find(x);
    public int getpar(int x) => find(x);
}