Problem:
Score : 700 points

Problem Statement

Ringo has an undirected graph G with N vertices numbered 1,2,...,N and M edges numbered 1,2,...,M.
Edge i connects Vertex a_{i} and b_{i} and has a length of w_i.

Now, he is in the middle of painting these N vertices in K colors numbered 1,2,...,K. Vertex i is already painted in Color c_i, except when c_i = 0, in which case Vertex i is not yet painted.

After he paints each vertex that is not yet painted in one of the K colors, he will give G to Snuke.

Based on G, Snuke will make another undirected graph G' with K vertices numbered 1,2,...,K and M edges.
Initially, there is no edge in G'. The i-th edge will be added as follows:

Let x and y be the colors of the two vertices connected by Edge i in G.

Add an edge of length w_i connecting Vertex x and y in G'.

What is the minimum possible sum of the lengths of the edges in the minimum spanning tree of G'? If G' will not be connected regardless of how Ringo paints the vertices, print -1.

Constraints

1 \leq N,M \leq 10^{5}

1 \leq K \leq N

0 \leq c_i \leq K

1 \leq a_i,b_i \leq N

1 \leq w_i \leq 10^{9}

The given graph may NOT be simple or connected.

All input values are integers.

Partial Scores

In the test set worth 100 points, N = K and c_i = i.

In the test set worth another 100 points, c_i \neq 0.

In the test set worth another 200 points, c_i = 0.

Input

Input is given from Standard Input in the following format:

N M K
c_1 c_2 ... c_{N}
a_1 b_1 w_1
:
a_M b_M w_M

Output

Print the answer.

Sample Input 1

4 3 3
1 0 1 2
1 2 10
2 3 20
2 4 50

Sample Output 1

60

G' will only be connected when Vertex 2 is painted in Color 3.

Sample Input 2

5 2 4
0 0 0 0 0
1 2 10
2 3 10

Sample Output 2

-1

Regardless of how Ringo paints the vertices, two edges is not enough to connect four vertices as one.

Sample Input 3

9 12 9
1 2 3 4 5 6 7 8 9
6 9 9
8 9 6
6 7 85
9 5 545631016
2 1 321545
1 6 33562944
7 3 84946329
9 7 15926167
4 7 53386480
5 8 70476
4 6 4549
4 8 8

Sample Output 3

118901402

Sample Input 4

18 37 12
5 0 4 10 8 7 2 10 6 0 9 12 12 11 11 11 0 1
17 1 1
11 16 7575
11 15 9
10 10 289938980
5 10 17376
18 4 1866625
8 11 959154208
18 13 200
16 13 2
2 7 982223
12 12 9331
13 12 8861390
14 13 743
2 10 162440
2 4 981849
7 9 1
14 17 2800
2 7 7225452
3 7 85
5 17 4
2 13 1
10 3 45
1 15 973
14 7 56553306
16 17 70476
7 18 9
9 13 27911
18 14 7788322
11 11 8925
9 13 654295
2 10 9
10 1 545631016
3 4 5
17 12 1929
2 11 57
1 5 4
1 17 7807368

Sample Output 4

171

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;

class Solver
{
    public Scanner sc;
    public void Solve()
    {
        int N, M,K;
        sc.Make(out N, out M, out K);
        var C = sc.ArrInt;
        var edge = new List<(int f, int t, long w)>();
        for (int i = 0; i < M; i++)
        {
            int a, b, w;
            sc.Make(out a, out b, out w);
            a--;b--;
            edge.Add((a, b, w));
        }
        //同じ色の頂点を縮約
        for(int i = 0; i < N; i++)
        {
            if (C[i] > 0) edge.Add((C[i] - 1 + N, i, 0));
        }
        var uf = new UnionFind(N + K);
        var res = 0L;
        var ct = 0;
        edge.Sort((a, b) => a.w.CompareTo(b.w));
        //終了状態において，色がまだ塗られていない頂点の色を既に色が塗られている頂点と被らないように塗ることができる
        foreach(var e in edge)
        {
            if (uf[e.f] == uf[e.t]) continue;
            if (e.w != 0) ct++;
            res += e.w;
            uf.Union(e.f, e.t);
            if (ct == K - 1) break;
        }
        if (ct != K - 1) Fail(-1);
        Console.WriteLine(res);
    }
}

public class UnionFind
{
    public int GroupCount { get; private set; }
    protected int[] data;
    public virtual int this[int i] => Find(i);
    public UnionFind(int size)
    {
        data = Create(size, () => -1);
        GroupCount = size;
    }
    protected int Find(int i)
        => data[i] < 0 ? i : (data[i] = Find(data[i]));
    public int Size(int i)
        => -data[Find(i)];
    public virtual bool Union(int u, int v)
    {
        u = Find(u); v = Find(v);
        if (u == v) return false;
        if (data[u] > data[v])
            swap(ref u, ref v);
        GroupCount--;
        data[u] += data[v];
        data[v] = u;
        return true;
    }
}
#region Template
public static class Template
{
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver() { sc = new Scanner() };
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        sol.Solve();
        Console.Out.Flush();
    }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    //public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    //public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    //public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion