Problem:
Score : 500 points

Problem Statement

In Takahashi Kingdom, which once existed, there are N cities, and some pairs of cities are connected bidirectionally by roads.
The following are known about the road network:

People traveled between cities only through roads. It was possible to reach any city from any other city, via intermediate cities if necessary.

Different roads may have had different lengths, but all the lengths were positive integers.

Snuke the archeologist found a table with N rows and N columns, A, in the ruin of Takahashi Kingdom.
He thought that it represented the shortest distances between the cities along the roads in the kingdom.

Determine whether there exists a road network such that for each u and v, the integer A_{u, v} at the u-th row and v-th column of A is equal to the length of the shortest path from City u to City v.
If such a network exist, find the shortest possible total length of the roads.

Constraints

1 \leq N \leq 300

If i ≠ j, 1 \leq A_{i, j} = A_{j, i} \leq 10^9.

A_{i, i} = 0

Inputs

Input is given from Standard Input in the following format:

N
A_{1, 1} A_{1, 2} ... A_{1, N}
A_{2, 1} A_{2, 2} ... A_{2, N}
...
A_{N, 1} A_{N, 2} ... A_{N, N}

Outputs

If there exists no network that satisfies the condition, print -1.
If it exists, print the shortest possible total length of the roads.

Sample Input 1

3
0 1 3
1 0 2
3 2 0

Sample Output 1

3

The network below satisfies the condition:

City 1 and City 2 is connected by a road of length 1.

City 2 and City 3 is connected by a road of length 2.

City 3 and City 1 is not connected by a road.

Sample Input 2

3
0 1 3
1 0 1
3 1 0

Sample Output 2

-1

As there is a path of length 1 from City 1 to City 2 and City 2 to City 3, there is a path of length 2 from City 1 to City 3.
However, according to the table, the shortest distance between City 1 and City 3 must be 3.

Thus, we conclude that there exists no network that satisfies the condition.

Sample Input 3

5
0 21 18 11 28
21 0 13 10 26
18 13 0 23 13
11 10 23 0 17
28 26 13 17 0

Sample Output 3

82

Sample Input 4

3
0 1000000000 1000000000
1000000000 0 1000000000
1000000000 1000000000 0

Sample Output 4

3000000000

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;
        long[,] A;
        void Solve() {
            N = io.Int;
            A = new long[N, N];
            N.REP(i => N.REP(j => A[i, j] = io.Long));

            var wf = new WarshallFloyd();
            wf.Init(N);
            N.REP(i => N.REP(j => wf.AddPath(i+1,j+1,A[i,j])));
            wf.Run();
            bool f = true;
            N.REP(i => N.REP(j => {
                if (wf.isMinPath(i+1,j+1,A[i,j])){
                    //
                }else{
                    f = false;
                }
            }));
            long ans = 0;

            ans=wf.orignCost();

            io.o(f ? ans : -1);
        }


        ////////////////////////////////////////////////////////////
        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 Dictionary<long, long> PrimeFactor(long n) {
            var ret = new Dictionary<long, long>();
            for (int i = 2; i * i <= n; ++i) {
                if (!ret.ContainsKey(i)) ret[i] = 0;
                while (n % i == 0) {
                    ++ret[i];
                    n /= i;
                }
            }
            return ret.Where(kp => kp.Value != 0).ToDictionary(kp => kp.Key, kp => kp.Value);
        }
        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<string[]> enuPart(string str) {
            var s = new Stack<Tuple<string, List<string>, int>>();
            s.Push(Tuple.Create(str[0].ToString(), new List<string>(), 1));
            while (s.Count > 0) {
                var cur = s.Pop();
                if (cur.Item3 >= str.Length) yield return (new List<string>(cur.Item2) { cur.Item1 }).ToArray();
                else {
                    s.Push(Tuple.Create(cur.Item1 + str[cur.Item3], new List<string>(cur.Item2), cur.Item3 + 1));
                    s.Push(Tuple.Create(str[cur.Item3].ToString(), new List<string>(cur.Item2) { cur.Item1 }, 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 {
        protected int I = -1;
        protected int V;
        protected int E;
        public long INF = (long)1e15;
        protected bool isNonDir = true;
        public long[] cost;
        public List<Tuple<int, long>>[] Adj;
        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 WF : ShortestPath {
        public WF() { }
        //
    }
    class WarshallFloyd {
        private int E;
        private bool isNonDir;
        public long INF = (long)1e15;
        public long[,] BefG;
        public long[,] G;
        public WarshallFloyd(bool isNonDir = true) {
            this.isNonDir = isNonDir;
        }
        public void Init(int n) {
            E = n + 1;
            G = new long[E, E];
            BefG = new long[E, E];
            for (int i = 0; i < E; ++i)
                for (int j = 0; j < E; ++j) {
                    G[i, j] = INF;
                    BefG[i, j] = INF;
                }
            for (int i = 0; i < E; ++i) {
                G[i, i] = 0;
                BefG[i, i] = 0;
            }
        }
        public void AddPath(int f, int t, long c) {
            if (isNonDir) {
                G[f, t] = c; G[t, f] = c;
                BefG[f, t] = c; BefG[t, f] = c;
            } else {
                G[f, t] = c;
                BefG[f, t] = c;
            }
        }
        public void AddPath(int[] f, int[] t) {
            for (int i = 0; i < f.Length; ++i)
                AddPath(f[i], t[i], 1);
        }
        public void AddPath(int[] f, int[] t, long[] c) {
            for (int i = 0; i < f.Length; ++i)
                AddPath(f[i], t[i], c[i]);
        }
        public void Run() {
            G = MinCostArr();
        }
        public long[,] MinCostArr() {
            for (int i = 0; i < E; ++i)
                for (int j = 0; j < E; ++j)
                    for (int k = 0; k < E; ++k)
                        G[j, k] = Math.Min(G[j, k], G[j, i] + G[i, k]);
            return G;
        }
        public int[] MinPath(int from, int to) {//TODO:test
            var ret = new List<int>();
            var cur = from;
            while (cur != to) {
                ret.Add(cur);
                for (int i = 1; i < E; ++i) {
                    if (BefG[cur, i] + G[i, to] == G[cur, to]) {
                        if (i == cur) continue;
                        cur = i;
                        break;
                    }
                }
            }
            ret.Add(cur);
            return ret.ToArray();
        }
        public bool isMinPath(int a, int b, long c) {
            for (int i = 1; i < E; ++i)
                if (G[i, a] + c == G[i, b])
                    return true;
            return false;
        }
        public long orignCost() {//test
            long orig = 0;
            for (int i = 1; i < E; ++i)
                for (int j = i+1; j < E; ++j) {
                    bool isOrig = true;
                    for (int k = 1; k < E; ++k)
                        if (k!=i&&k!=j&&G[i, j] == G[i, k] + G[k, j]) {
                            isOrig = false;   
                        }
                    if(isOrig)
                        orig += BefG[i, j];
                }
            return orig;
        }
    }
    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)); }
        public static int[] toIntArr(this string[] a) { return Array.ConvertAll(a, int.Parse); }
        public static long[] toLongArr(this string[] a) { return Array.ConvertAll(a, long.Parse); }
        public static double[] toDoubleArr(this string[] a) { return Array.ConvertAll(a, double.Parse); }
        public static char[] toCharArr(this string[] a) { return Array.ConvertAll(a, char.Parse); }
    }
    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
}