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: Time Limit Exceeded)

using System;
using System.Text;
using System.Linq;
using System.Collections.Generic;

class Program
{
    private static readonly Scanner sc = new Scanner();
    static void Main(string[] args)
    {
        int n = sc.Int;
        int m = sc.Int;

        BellmanFord bf = new BellmanFord(n);

        for (int i = 0; i < m; i++)
            bf.AddEdge(sc.Int-1, sc.Int-1, -sc.Int);

        bf.CalcDistance(0);

        Console.WriteLine(bf.IsNegInf(n-1) ? "inf" : (-bf.GetDistance(n-1)).ToString());
    }
}

class Scanner
{
    private string[] _str = new string[0];
    private int _i;

    public string Line { get { return Console.ReadLine(); } }

    public string Str
    {
        get
        {
            if (_i >= _str.Length)
            {
                _str = Line.Split(' ');
                _i = 0;
            }
            return _str[_i++];
        }
    }

    public string[] StrArr { get { return Line.Split(' '); } }
    public int Int { get { return int.Parse(Str); } }
    public int[] IntArr { get { return Line.Split(' ').Select(int.Parse).ToArray(); } }
    public long Long { get { return long.Parse(Str); } }
    public long[] LongArr { get { return Line.Split(' ').Select(long.Parse).ToArray(); } }
    public double Double { get { return double.Parse(Str); } }
    public double[] DoubleArr { get { return Line.Split(' ').Select(double.Parse).ToArray(); } }
}



class BellmanFord
{
    private class Edge
    {
        public int To;
        public long Cost;
    }

    private readonly int _n;
    private readonly List<Edge>[] _g;
    private readonly long[] _dist;
    private readonly bool[] _negloop;
    private readonly bool[] _visited;

    public bool NegLoopExist;

    public BellmanFord(int n)
    {
        _n = n;
        _g = new List<Edge>[n];
        _dist = new long[n];
        _negloop = new bool[n];
        _visited = new bool[n];

        for (var i = 0; i < n; i++)
            _g[i] = new List<Edge>();
    }

    public void AddEdge(int from, int to, int cost)
    {
        _g[from].Add(new Edge {To = to, Cost = cost});
    }

    public void CalcDistance(int s)
    {
        for (var i = 0; i < _n; i++)
        {
            _dist[i] = long.MaxValue;
            _visited[i] = false;
            _negloop[i] = false;
        }
        _dist[s] = 0;

        var q = new Queue<int>(_n);
        q.Enqueue(s);
        var cnt = 0;

        while (q.Count != 0 && cnt < _n * 2)
        {
            var update = false;
            var qn = new Queue<int>(_n);
            while (q.Count != 0)
            {
                var v = q.Dequeue();
                _visited[v] = true;
                foreach (var e in _g[v])
                {
                    var newdist = _dist[v] + e.Cost;
                    if (_dist[e.To] > newdist)
                    {
                        _dist[e.To] = newdist;
                        qn.Enqueue(e.To);
                        update = true;

                        if (cnt >= _n - 1)
                            _negloop[v] = _negloop[e.To] = true;
                    }
                }
            }
            q = qn;
            if (update)
                cnt++;
        }

        if (cnt >= _n)
            NegLoopExist = true;
    }

    public long GetDistance(int i)
    {
        return _dist[i];
    }

    public bool IsNegInf(int i)
    {
        return _negloop[i];
    }

    public bool IsReachable(int i)
    {
        return _visited[i];
    }
}