Problem:
Score : 400 points

Problem Statement

There is a directed graph with N vertices and M edges.
The i-th edge (1≤i≤M) points from vertex a_i to vertex b_i, and has a weight c_i.
We will play the following single-player game using this graph and a piece.

Initially, the piece is placed at vertex 1, and the score of the player is set to 0.
The player can move the piece as follows:

When the piece is placed at vertex a_i, move the piece along the i-th edge to vertex b_i. After this move, the score of the player is increased by c_i.

The player can end the game only when the piece is placed at vertex N.
The given graph guarantees that it is possible to traverse from vertex 1 to vertex N.

When the player acts optimally to maximize the score at the end of the game, what will the score be?
If it is possible to increase the score indefinitely, print inf.

Constraints

2≤N≤1000

1≤M≤min(N(N-1),2000)

1≤a_i,b_i≤N (1≤i≤M)

a_i≠b_i (1≤i≤M)

a_i≠a_j or b_i≠b_j (1≤i<j≤M)

-10^9≤c_i≤10^9 (1≤i≤M)

c_i is an integer.

In the given graph, there exists a path from vertex 1 to vertex N.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf.

Sample Input 1

3 3
1 2 4
2 3 3
1 3 5

Sample Output 1

7

There are two ways to move the piece to vertex N=3:

vertex 1 → vertex 2 → vertex 3 : score 4+3=7

vertex 1 → vertex 3 : score 5

Thus, the maximum possible score at the end of the game is 7.

Sample Input 2

2 2
1 2 1
2 1 1

Sample Output 2

inf

It is possible to increase the score indefinitely by alternating between vertex 1 and 2.

Sample Input 3

6 5
1 2 -1000000000
2 3 -1000000000
3 4 -1000000000
4 5 -1000000000
5 6 -1000000000

Sample Output 3

-5000000000

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, M;
        public Graph G;
        public void Run()
        {
            // Input
            {
                var line = Input.ReadIntArray();
                N = line[0];
                M = line[1];
            }

            // Graph
            G = new Graph(N);
            for (int i = 0; i < M; i++)
            {
                var line = Input.ReadIntArray();
                int u = line[0] - 1;
                int v = line[1] - 1;
                long d = -line[2];

                // 無向グラフ
                var e1 = new Edge(u, v, d);
                G[u].Edges.Add(e1);
            }

            G[0].Dist = 0;

            // bellman-ford
            for (int t = 0; t < N; t++)
            {
                for (int i = 0; i < N; i++)
                {
                    var node = G[i];
                    if (node.Dist == long.MaxValue) continue;
                    foreach (var edge in node.Edges)
                    {
                        G[edge.To].Dist = Math.Min(G[edge.To].Dist, edge.Cost + node.Dist);
                    }
                }
            }

            long distN = G[N - 1].Dist;

            // another loops
            for (int t = 0; t < N; t++)
            {
                for (int i = 0; i < N; i++)
                {
                    var node = G[i];
                    if (node.Dist == long.MaxValue) continue;
                    foreach (var edge in node.Edges)
                    {
                        G[edge.To].Dist = Math.Min(G[edge.To].Dist, edge.Cost + node.Dist);
                    }
                }
            }

            if (distN == G[N - 1].Dist)
            {
                Console.WriteLine(-distN);
            }
            else
            {
                Console.WriteLine("inf");
            }
        }

    }

    internal class Graph
    {
        public List<Node> Nodes;

        public Node this[int i]
        {
            set { Nodes[i] = value; }
            get { return Nodes[i]; }
        }

        public Graph(int N)
        {
            Nodes = new List<Node>();
            for (int i = 0; i < N; i++)
            {
                Nodes.Add(new Node(i));
            }
        }

    }

    internal class Node
    {
        public List<Edge> Edges;
        public long Dist;
        public int No;

        public Node(int no)
        {
            this.No = no;
            Dist = long.MaxValue;
            Edges = new List<Edge>();
        }
    }

    internal class Edge
    {
        public int From;
        public int To;
        public long Cost;
        public Edge Rev;

        public Edge(int fr, int to, long cost = 0)
        {
            From = fr;
            To = to;
            Cost = cost;
        }

        public bool IsRev(Edge e)
        {
            return Rev != null && (e == Rev);
        }
    }

    // 通常はIComparableのみが必要
    class EdgeData : IComparable<EdgeData>, IComparable
    {
        public long Dist;
        public Edge Edge;
        public EdgeData(long dist, Edge edge)
        {
            Dist = dist;
            Edge = edge;
        }

        public int CompareTo(EdgeData other)
        {
            return Dist.CompareTo(other.Dist);
        }

        public int CompareTo(object obj)
        {
            if (obj == null) return 1;
            if (GetType() != obj.GetType()) throw new ArgumentException();
            return CompareTo((EdgeData)obj);
        }
    }



    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}