Problem:
Score : 400 points

Problem Statement

Dolphin is planning to generate a small amount of a certain chemical substance C.

In order to generate the substance C, he must prepare a solution which is a mixture of two substances A and B in the ratio of M_a:M_b.

He does not have any stock of chemicals, however, so he will purchase some chemicals at a local pharmacy.

The pharmacy sells N kinds of chemicals. For each kind of chemical, there is exactly one package of that chemical in stock.

The package of chemical i contains a_i grams of the substance A and b_i grams of the substance B, and is sold for c_i yen (the currency of Japan).

Dolphin will purchase some of these packages. For some reason, he must use all contents of the purchased packages to generate the substance C.

Find the minimum amount of money required to generate the substance C.

If it is not possible to generate the substance C by purchasing any combination of packages at the pharmacy, report that fact.

Constraints

1≦N≦40

1≦a_i,b_i≦10

1≦c_i≦100

1≦M_a,M_b≦10

gcd(M_a,M_b)=1

a_i, b_i, c_i, M_a and M_b are integers.

Input

The input is given from Standard Input in the following format:

N M_a M_b
a_1 b_1 c_1
a_2 b_2 c_2
:
a_N b_N c_N

Output

Print the minimum amount of money required to generate the substance C. If it is not possible to generate the substance C, print -1 instead.

Sample Input 1

3 1 1
1 2 1
2 1 2
3 3 10

Sample Output 1

3

The amount of money spent will be minimized by purchasing the packages of chemicals 1 and 2.

In this case, the mixture of the purchased chemicals will contain 3 grams of the substance A and 3 grams of the substance B, which are in the desired ratio: 3:3=1:1.

The total price of these packages is 3 yen.

Sample Input 2

1 1 10
10 10 10

Sample Output 2

-1

The ratio 1:10 of the two substances A and B cannot be satisfied by purchasing any combination of the packages. Thus, the output should be -1.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Linq.Expressions;
using System.Text;
namespace Program {
    class MainClass {
        ////////////////////////////////////////////////////////////
        int N, Ma, Mb;
        int[] a, b, c;
        const int INF = 1234567890;
        void Solve() {
            io.i(out N, out Ma, out Mb);
            io.ini(out a, out b, out c, N);
            int[,,] dp = new int[N + 1, (N + 1) * a.Max() + 1, (N + 1) * b.Max() + 1];
            for (int i = 0; i < dp.GetLength(0); ++i)
                for (int j = 0; j < dp.GetLength(1); ++j)
                    for (int k = 0; k < dp.GetLength(2); ++k)
                        dp[i, j, k] = INF;
            dp[0, 0, 0] = 0;
            for (int i = 0; i < dp.GetLength(0) - 1; ++i) {
                for (int j = 0; j < dp.GetLength(1); ++j) {
                    for (int k = 0; k < dp.GetLength(2); ++k) {
                        if (dp[i, j, k] != INF) {
                            dp[i + 1, j, k] = Math.Min(dp[i + 1, j, k], dp[i, j, k]);
                            dp[i + 1, j + a[i], k + b[i]] =
                                Math.Min(dp[i, j, k] + c[i], dp[i + 1, j + a[i], k + b[i]]);
                        }

                    }
                }
            }
            int ans = INF;
            for (int i = 1; i < dp.GetLength(1); ++i) {
                for (int j = 1; j < dp.GetLength(2); ++j) {
                    if (ratio(i, j))
                        ans = Math.Min(ans, dp[N, i, j]);
                }
            }
            if (ans == INF) {
                io.o(-1);
            } else {
                io.o(ans);
            }

        }
        bool ratio(int a, int b) {
            return a * Mb == b * Ma;
        }

        ////////////////////////////////////////////////////////////
        public static void Main() { new MainClass().Stream(); }
        IO io = new IO();
        void Stream() { Solve(); io.writeFlush(); }
        //void Stream() { Test(); io.writeFlush(); }
        void Test() { }
        #region MockMacro
        //cannot use break,continue,goto
        void FOR(int a, int b, Action<int> act) { for (int i = a; i < b; ++i) act(i); }
        void FORR(int a, int b, Action<int> act) { for (int i = a - 1; i >= b; --i) act(i); }
        #endregion
        ////////////////////////////////////////////////////////////
    }
    #region default
    class IO {
        string[] nextBuffer;
        int BufferCnt;
        char[] cs = new char[] { ' ' };
        StreamWriter sw = new StreamWriter(Console.OpenStandardOutput()) {
            AutoFlush = false
        };
        public IO() {
            nextBuffer = new string[0];
            BufferCnt = 0;
            Console.SetOut(sw);
        }
        public string Next() {
            if (BufferCnt < nextBuffer.Length)
                return nextBuffer[BufferCnt++];
            string st = Console.ReadLine();
            while (st == "")
                st = Console.ReadLine();
            nextBuffer = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            BufferCnt = 0;
            return nextBuffer[BufferCnt++];
        }
        public string String => Next();
        public char Char => char.Parse(String);
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
        public string[] arr => Console.ReadLine().Split(' ');
        public char[] arrChar => Array.ConvertAll(arr, char.Parse);
        public int[] arrInt => Array.ConvertAll(arr, int.Parse);
        public long[] arrLong => Array.ConvertAll(arr, long.Parse);
        public double[] arrDouble => Array.ConvertAll(arr, double.Parse);
        public T i<T>() { return suitType<T>(String); }
        public void i<T>(out T v) { v = suitType<T>(String); }
        public void i<T, U>(out T v1, out U v2) { i(out v1); i(out v2); }
        public void i<T, U, V>(out T v1, out U v2, out V v3) { i(out v1); i(out v2); i(out v3); }
        public void i<T, U, V, W>(out T v1, out U v2, out V v3, out W v4) {
            i(out v1); i(out v2); i(out v3); i(out v4);
        }
        public void i<T, U, V, W, X>(out T v1, out U v2, out V v3, out W v4, out X v5) {
            i(out v1); i(out v2); i(out v3); i(out v4); i(out v5);
        }
        public void ini<T>(out T[] a, int n) {
            a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = suitType<T>(String);
        }
        public void ini<T, U>(out T[] a, out U[] b, int n) {
            a = new T[n]; b = new U[n];
            for (int i = 0; i < n; ++i) { a[i] = i<T>(); b[i] = i<U>(); }
        }
        public void ini<T, U, V>(out T[] a, out U[] b, out V[] c, int n) {
            a = new T[n]; b = new U[n]; c = new V[n];
            for (int i = 0; i < n; ++i) { a[i] = i<T>(); b[i] = i<U>(); c[i] = i<V>(); }
        }
        public void ini<T>(out T[,] a, int h, int w) {
            a = new T[h, w];
            for (int i = 0; i < h; ++i) for (int j = 0; j < w; ++j) a[i, j] = i<T>();
        }
        public void o<T>(T v) { Console.WriteLine(v); }
        public void o<T>(params T[] a) { Array.ForEach(a, n => o(n)); }
        public void o<T>(T[,] a) {
            int a0 = a.GetLength(0), a1 = a.GetLength(1);
            for (int i = 0; i < a0; ++i) {
                for (int j = 0; j < a1 - 1; ++j)
                    Console.Write(a[i, j] + " ");
                Console.WriteLine(a[i, a1 - 1]);
            }
        }
        public void ol<T>(params T[] a) { o(connect<T>(a)); }
        public void or<T>(T a) { Console.Write(a); }
        public void br() { o(""); }
        public void writeFlush() { Console.Out.Flush(); }
        private string connect<T>(params T[] s) { return string.Join(" ", s); }
        private bool typeEQ<T, U>() { return typeof(T).Equals(typeof(U)); }
        private T convertType<T, U>(U v) { return (T)Convert.ChangeType(v, typeof(T)); }
        private T suitType<T>(string s) {
            if (typeEQ<T, int>()) return convertType<T, int>(int.Parse(s));
            if (typeEQ<T, long>()) return convertType<T, long>(long.Parse(s));
            if (typeEQ<T, double>()) return convertType<T, double>(double.Parse(s));
            if (typeEQ<T, char>()) return convertType<T, char>(char.Parse(s));
            return convertType<T, string>(s);
        }
    }
    class PQueue<T> where T : IComparable {
        public List<T> heap; private Comparison<T> comp; private IComparer<T> comparer;
        private int size; private int type;//type=0->min
        public PQueue(int type = 0) : this(Comparer<T>.Default) { this.type = type; }
        public PQueue(IComparer<T> comparer) : this(16, comparer.Compare) { this.comparer = comparer; }
        public PQueue(Comparison<T> comparison) : this(16, comparison) { }
        public PQueue(int capacity, Comparison<T> comparison) { this.heap = new List<T>(capacity); this.comp = comparison; }
        public void Enqueue(T item) {
            this.heap.Add(item); var i = size++;
            while (i > 0) { var p = (i - 1) >> 1; if (Compare(this.heap[p], item) <= 0) break; this.heap[i] = heap[p]; i = p; }
            this.heap[i] = item;
        }
        public T Dequeue() {
            var ret = this.heap[0]; var x = this.heap[--size]; var i = 0;
            while ((i << 1) + 1 < size) {
                var a = (i << 1) + 1; var b = (i << 1) + 2; if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                if (Compare(heap[a], x) >= 0) break; heap[i] = heap[a]; i = a;
            }
            heap[i] = x; heap.RemoveAt(size);
            return ret;
        }
        public T Peek() { return heap[0]; }
        public int Count { get { return size; } }
        public bool Any() { return size > 0; }
        public bool Empty() { return !Any(); }
        public bool Contains(T v) { return heap.Contains(v); }
        private int Compare(T x, T y) { return type == 0 ? x.CompareTo(y) : y.CompareTo(x); }
    }
    #endregion
    #region other
    class Mat {
        public long mod = 1000000007;//10^9+7
        public long Pow(long a, long b) {
            if (b == 0) return 1;
            if (b % 2 == 1) return (a % mod * Pow(a % mod, b - 1) % mod) % mod;
            else return Pow(a * a % mod, b / 2) % mod;
        }
        public long Fact(long n) {
            long ret = 1;
            for (long i = 1; i <= n; i++) ret = (ret * i) % mod;
            return ret;
        }
        public long ModC(long n, long r) {
            if (r == 0 || n == r) return 1;
            if (n == 0) return 0;
            if (n < 0 || n < r) throw new ArgumentException("n,r invalid");
            else return (Fact(n) % mod * Pow((Fact(n - r) % mod * Fact(r) % mod) % mod, mod - 2) % mod) % mod;
        }
        public long[,] C(int N) {
            long[,] Co = new long[N + 1, N + 1];
            (N + 1).REP(i => (i + 1).REP(j => Co[i, j] = (j == 0 || j == i) ? 1L : Co[i - 1, j - 1] + Co[i - 1, j]));
            return Co;
        }
        public long DupC(long n, long r) { return ModC(n + r - 1, r); }
        public long P(long n, long r) { return Fact(n) / (Fact(n - r)); }//test
        public bool isPrime(long n) {
            if (n == 2) return true; if (n < 2 || n % 2 == 0) return false;
            for (long v = 3; v <= (long)Math.Sqrt(n); v += 2) if (n % v == 0) return false;
            return true;
        }
        public long LCM(long a, long b) { return a * (b / GCD(a, b)); }
        public long LCM(params long[] a) { return a.Aggregate((v, n) => LCM(v, n)); }
        public long GCD(long a, long b) { if (a < b) Swap(ref a, ref b); return b == 0 ? a : GCD(b, a % b); }
        public long GCD(params long[] array) { return array.Aggregate((v, n) => GCD(v, n)); }
        public T Max<T>(params T[] a) { return a.Max(); }
        public T Min<T>(params T[] a) { return a.Min(); }
        public void Swap<T>(ref T a, ref T b) { T tmp = a; a = b; b = tmp; }
        public double Dis(int x1, int y1, int x2, int y2) { return Math.Sqrt(Math.Pow((x2 - x1), 2) + Math.Pow((y2 - y1), 2)); }
        public int mDis(int x1, int y1, int x2, int y2) { return Math.Abs(x1 - x2) + Math.Abs(y1 - y2); }
        public int[] DigArr(int n) { int[] ret = new int[Digit(n)]; ret.Length.REP(i => ret[i] = DigVal(n, i + 1)); return ret; }
        public long DigArr2Num(IEnumerable<int> enu) { return enu.Aggregate((v, n) => v * 10 + n); }
        public int Digit(long n) { return (n == 0) ? 1 : (int)Math.Log10(n) + 1; }
        public int DigVal(int n, int dig) { return (n % (int)Pow(10, dig)) / (int)Pow(10, dig - 1); }
        public long Tousa(long a, long d, long n) { return a + (n - 1) * d; }
        public long TousaSum(long a, long d, long n) { return n * (2 * a + (n - 1) * d) / 2; }
        public long[] enuDivsor(long N) {
            var ret = new SortedSet<long>();
            for (long i = 1; i * i <= N; i++)
                if (N % i == 0) { ret.Add(i); ret.Add(N / i); }
            return ret.ToArray();
        }
        public IEnumerable<int[]> enuP(int[] Arr, int Use = -1) {//列挙順列
            Use = (Use != -1) ? Use : Arr.Length;
            if (Use == 0 || Arr.Length < Use)
                yield break;
            var s = new Stack<List<int>>();
            for (int i = Arr.Length - 1; i >= 0; i--)
                s.Push(new List<int>() { i });
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Count == Use) {
                    var ret = new List<int>();
                    cur.ForEach(X => ret.Add(Arr[X]));
                    yield return ret.ToArray();
                } else
                    for (int i = Arr.Length - 1; i >= 0; i--)
                        if (!cur.Contains(i))
                            s.Push(new List<int>(cur) { i });
            }
        }
        public IEnumerable<int[]> enuC(int[] Arr, int Use = -1) {//列挙組み合わせ
            Use = (Use != -1) ? Use : Arr.Length;
            if (Use == 0 || Arr.Length < Use) yield break;
            var s = new Stack<Tuple<int, List<int>>>();
            Arr.Length.REPR(i => s.Push(Tuple.Create(i, new List<int>() { Arr[i] })));
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Item2.Count == Use) yield return cur.Item2.ToArray();
                else for (int i = Arr.GetUpperBound(0); i > cur.Item1; i--)
                        s.Push(Tuple.Create(i, new List<int>(cur.Item2) { Arr[i] }));
            }
        }
        public IEnumerable<int[]> enuDupP(int[] Arr, int Use = -1) {//列挙重複順列
            Use = (Use != -1) ? Use : Arr.Length; if (Use == 0) yield break; var s = new Stack<List<int>>();
            Arr.Length.REPR(i => s.Push(new List<int>() { Arr[i] }));
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Count == Use) yield return cur.ToArray();
                else Arr.Length.REPR(i => s.Push(new List<int>(cur) { Arr[i] }));
            }
        }
        public IEnumerable<int[]> enuDupC(int[] Arr, int Use = -1) {//列挙組み合わせ
            Use = (Use != -1) ? Use : Arr.Length; if (Use == 0) yield break;
            var s = new Stack<Tuple<int, List<int>>>();
            Arr.Length.REPR(i => s.Push(Tuple.Create(i, new List<int>() { Arr[i] })));
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Item2.Count == Use) yield return cur.Item2.ToArray();
                else for (int i = Arr.GetUpperBound(0); i >= cur.Item1; i--)
                        s.Push(Tuple.Create(i, new List<int>(cur.Item2) { Arr[i] }));
            }
        }
        public IEnumerable<long[]> enuPart(string str) {
            var s = new Stack<Tuple<string, List<long>, int>>();
            s.Push(Tuple.Create(str[0].ToString(), new List<long>(), 1));
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Item3 >= str.Length) yield return (new List<long>(cur.Item2) { cur.Item1.toLong() }).ToArray();
                else {
                    s.Push(Tuple.Create(cur.Item1 + str[cur.Item3], new List<long>(cur.Item2), cur.Item3 + 1));
                    s.Push(Tuple.Create(str[cur.Item3].ToString(), new List<long>(cur.Item2) { cur.Item1.toLong() }, cur.Item3 + 1));
                }
            }
        }
    }
    #endregion
    #region Data
    class AssociativeArray<T> : IEnumerable {
        public Dictionary<T, int> dic;
        public AssociativeArray() { dic = new Dictionary<T, int>(); }
        public AssociativeArray(params T[] a) { dic = new Dictionary<T, int>(); Add(a); }
        public void Add(T a) { if (!conK(a)) dic[a] = 0; dic[a]++; }
        public void Add(params T[] a) { a.Length.REP(i => { if (!conK(a[i])) dic[a[i]] = 0; dic[a[i]]++; }); }
        public void Set(T k, int v) { if (!dic.ContainsKey(k)) dic[k] = 0; dic[k] = v; }
        public void Remove(params T[] a) { a.Length.REP(i => { if (conK(a[i])) dic.Remove(a[i]); }); }
        public T[] Keys() { return dic.Keys.ToArray<T>(); }
        public int Val(T k) { return (dic.ContainsKey(k)) ? dic[k] : 0; }
        public int ValSum => dic.Values.Sum();
        public int KeyNum => dic.Keys.Count;
        public int MaxVal => dic.Values.Max();
        public int MinVal => dic.Values.Min();
        public T MaxKey => MaxK();
        public T MinKey => MinK();
        public T MaxK() { var maxV = MaxVal; return dic.First(d => d.Value == maxV).Key; }
        public T MinK() { var minV = MinVal; return dic.First(d => d.Value == minV).Key; }
        public T[] MaxKeys() {
            var maxV = MaxVal;
            return dic.Where(kp => kp.Value == maxV).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray();
        }
        public T[] MinKeys() {
            var minV = MinVal;
            return dic.Where(kp => kp.Value == minV).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray();
        }
        public bool conK(T k) { return dic.ContainsKey(k); }
        public bool anyK(params T[] k) { return k.Any(key => conK(key)); }
        public bool allK(params T[] k) { return k.All(key => conK(key)); }
        public void Show() { foreach (var v in dic) { Console.WriteLine(v.Key + " : " + v.Value); } }
        public IEnumerator GetEnumerator() { foreach (var kp in dic) yield return kp; }
        public T[] ValueSortedKey(bool inc = true) {//test
            return (inc ? (dic.OrderBy(kp => kp.Value)) : (dic.OrderByDescending(kp => kp.Value)))
                .ThenBy(kp => kp.Key).ToDictionary(kp => kp.Key, kp => kp.Value).Keys.ToArray();
        }
        //:sort->array
    }
    class TreeDis {//TODO:shortestPath
        public List<Tuple<long, long>>[] g; public long[] a2other; private int type;
        public TreeDis(int type = 0) { this.type = type; }//0->bfs,other->dfs
        public void Init(long n) { g = new List<Tuple<long, long>>[n + 1]; g.Length.REP(i => g[i] = new List<Tuple<long, long>>()); }
        public void Run(long[] a, long[] b) { a.Length.REP(i => { g[a[i]].Add(Tuple.Create(b[i], 1L)); g[b[i]].Add(Tuple.Create(a[i], 1L)); }); }
        public void Run(long[] a, long[] b, long[] w) { a.Length.REP(i => { g[a[i]].Add(Tuple.Create(b[i], w[i])); g[b[i]].Add(Tuple.Create(a[i], w[i])); }); }
        public long[] a2iArr(long a) { a2other = new long[g.Count()]; if (type == 0) BFS(a); else DFS(a); return a2other; }
        private void BFS(long a) {
            var q = new Queue<Tuple<long, long>>(); q.Enqueue(Tuple.Create(a, -1L));
            while (q.Count > 0) {
                var c = q.Dequeue();
                foreach (var v in g[c.Item1]) {
                    if (v.Item1 == c.Item2) continue;
                    a2other[v.Item1] = a2other[c.Item1] + v.Item2; q.Enqueue(Tuple.Create(v.Item1, c.Item1));
                }
            }
        }
        private void DFS(long a) {
            var s = new Stack<Tuple<long, long>>(); s.Push(Tuple.Create(a, -1L));
            while (s.Count > 0) {
                var c = s.Pop();
                foreach (var v in g[c.Item1]) {
                    if (v.Item1 == c.Item2) continue;
                    a2other[v.Item1] = a2other[c.Item1] + v.Item2; s.Push(Tuple.Create(v.Item1, c.Item1));
                }
            }
        }
    }
    class ShortestPath {
        public long INF = (long)1e15; protected int I = -1; protected int V; protected int E; public long[] cost;
        public List<Tuple<int, long>>[] Adj; protected bool isNonDir = true;
        public void Init(int n) { I = n + 1; V = n; Adj = new List<Tuple<int, long>>[I]; I.REP(i => Adj[i] = new List<Tuple<int, long>>()); }
        public void AddPath(int f, int t, long c) {
            E++;
            if (isNonDir) {
                Adj[f].Add(Tuple.Create(t, c)); Adj[t].Add(Tuple.Create(f, c));
            } else {
                Adj[f].Add(Tuple.Create(t, c));
            }
        }
        public void AddPath(int[] f, int[] t, long[] c) { f.Length.REP(i => AddPath(f[i], t[i], c[i])); }
    }
    class Dijkstra : ShortestPath {//隣接対応後検証不足,有向とか
        public long MinCost(int f, int t) {
            cost = new long[I]; cost.Set(INF); cost[f] = 0;
            var pq = new PQueue<Tuple<int, long>>(); pq.Enqueue(Tuple.Create(f, 0L));//(from,cost)
            while (pq.Count > 0) {
                var cur = pq.Dequeue();
                if (cost[cur.Item1] < cur.Item2) continue; Adj[cur.Item1].Count.REP(i => {
                    var tmp = Adj[cur.Item1][i];
                    if (cost[tmp.Item1] > cost[cur.Item1] + tmp.Item2) {
                        cost[tmp.Item1] = cost[cur.Item1] + tmp.Item2; pq.Enqueue(Tuple.Create(tmp.Item1, cost[tmp.Item1]));
                    }
                });
            }
            return cost[t];
        }
    }
    class BellmanFord : ShortestPath {
        private bool[] neg;
        public BellmanFord() { }
        public BellmanFord(bool isNonDir) { this.isNonDir = isNonDir; }
        public long MinCost(int f, int t) {
            cost = new long[I]; cost.Set(INF); cost[f] = 0; neg = new bool[I];
            for (int i = 0; i < I - 1; i++) {
                I.REP(j => Adj[j].Count.REP(k => {
                    var cur = Adj[j][k];
                    if (cost[cur.Item1] > cost[j] + cur.Item2)
                        cost[cur.Item1] = cost[j] + cur.Item2;
                }));
            }
            for (int i = 0; i < I; i++) {
                I.REP(j => Adj[j].Count.REP(k => {
                    var cur = Adj[j][k];
                    if (cost[cur.Item1] > cost[j] + cur.Item2) {
                        cost[cur.Item1] = cost[j] + cur.Item2;
                        neg[cur.Item1] = true;
                    }
                    if (neg[j]) neg[cur.Item1] = true;
                }));
            }
            return cost[t];
        }
        public bool loopExist() { return neg[I - 1]; }
    }
    class WarshallFloyd {//そのうちAdjとどっちがいいか...TODO:ジェネリック
        private int E; private int INF = (int)1e9; public long[,] G;
        public void Init(int n) { E = n + 1; G = new long[E, E]; G.Set(INF); E.REP(i => G[i, i] = 0); }
        public void AddPath(int f, int t, long c) { G[f, t] = c; G[t, f] = c; }
        public void AddPath(int[] f, int[] t) { f.Length.REP(i => AddPath(f[i], t[i], 1)); }
        public void AddPath(int[] f, int[] t, long[] c) { f.Length.REP(i => AddPath(f[i], t[i], c[i])); }
        public void Run() { G = MinCostArr(); }
        public long[,] MinCostArr() { E.REP(i => E.REP(j => E.REP(k => G[j, k] = Math.Min(G[j, k], G[j, i] + G[i, k])))); return G; }
    }
    class UnionFind {
        public long[] parent; public long[] depth; private int I;
        public void Init(int n) { I = n + 1; parent = new long[I]; depth = new long[I]; I.REP(i => parent[i] = i); }
        public long Find(long x) { return (parent[x] == x) ? x : parent[x] = Find(parent[x]); }
        public void Unite(long x, long y) {
            x = Find(x); y = Find(y); if (x == y) return;
            if (depth[x] < depth[y]) parent[x] = y; else { parent[y] = x; if (depth[x] == depth[y]) depth[x]++; }
        }
        public bool Same(int a, int b) { return Find(a) == Find(b); }
        public long Size(int x) { return depth[Find(x)]; }
    }
    class Kruskal : ShortestPath {
        public long Run() {
            var L = new List<Tuple<int, int, long>>();
            for (int i = 0; i < I; ++i)
                foreach (var t in Adj[i])
                    L.Add(Tuple.Create(i, t.Item1, t.Item2));
            L = L.OrderBy(t => t.Item3).ToList();
            var uf = new UnionFind();
            uf.Init(V); long ret = 0;
            foreach (var t in L)
                if (!uf.Same(t.Item1, t.Item2)) {
                    ret += t.Item3;
                    uf.Unite(t.Item1, t.Item2);
                }
            return ret;
        }
    }
    #endregion
    #region Ex
    static class StringEX {
        public static string Reversed(this string s) { return string.Join("", s.Reverse()); }
        public static string Repeat(this string s, int n) { return string.Concat(Enumerable.Repeat(s, n).ToArray()); }
        public static int toInt(this string s) { int n; return (int.TryParse(s.TrimStart('0'), out n)) ? n : 0; }
        public static int toInt(this char c) { return toInt(c.ToString()); }
        public static int toInt(this char[] c) { return toInt(new string(c)); }
        public static long toLong(this string s) { long n; return (long.TryParse(s.TrimStart('0'), out n)) ? n : (long)0; }
        public static long toLong(this char c) { return toLong(c.ToString()); }
        public static long toLong(this char[] c) { return toLong(new string(c)); }
        public static string toString(this char[] c) { return new string(c); }
    }
    static class NumericEx {
        public static string pad0<T>(this T v, int n) { return v.ToString().PadLeft(n, '0'); }
        public static double RoundOff(this double v, int n) { return Math.Round(v, n - 1, MidpointRounding.AwayFromZero); }
        public static bool Odd(this int v) { return v % 2 != 0; }
        public static bool Odd(this long v) { return v % 2 != 0; }
        public static void REP(this int v, Action<int> act) { for (int i = 0; i < v; ++i) act(i); }
        public static void REPR(this int v, Action<int> act) { for (int i = v - 1; i >= 0; --i) act(i); }
    }
    static class ArrayEX {
        public static T[] Sort<T>(this T[] a) { Array.Sort(a); return a; }
        public static T[] SortR<T>(this T[] a) { Array.Sort(a); Array.Reverse(a); return a; }
        public static void Set<T>(this T[] a, T v) { a.Length.REP(i => a[i] = v); }
        public static void Set<T>(this T[,] a, T v) { a.GetLength(0).REP(i => a.GetLength(1).REP(j => a[i, j] = v)); }
    }
    static class BitEx {
        public static bool Any(this BitArray b) { foreach (bool f in b) if (f) return true; return false; }
        public static bool All(this BitArray b) { foreach (bool f in b) if (!f) return false; return true; }
        public static bool None(this BitArray b) { return !Any(b); }
        public static void Flip(this BitArray b, int index) { b.Set(index, !b.Get(index)); }
    }
    static class IEnumerableEx {
        //
    }
    #endregion
}