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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'prime'
require 'set'
require 'tsort'
include Math
def max(a,b);              a > b ? a : b                              end
def min(a,b);              a < b ?  a : b                             end
def swap(a,b);             a, b = b, a                                end
def gif;                   gets.to_i                                  end
def gff;                   gets.to_f                                  end
def gsf;                   gets.chomp                                 end
def gi;                    gets.split.map(&:to_i)                     end
def gf;                    gets.split.map(&:to_f)                     end
def gs;                    gets.chomp.split.map(&:to_s)               end
def gc;                    gets.chomp.split('')                       end
def pr(num);               num.prime_division                         end
def digit(num);            num.to_s.length                            end
def array(s,ini=nil);      Array.new(s){ini}                          end
def darray(s1,s2,ini=nil); Array.new(s1){Array.new(s2){ini}}          end
def rep(num);              num.times{|i|yield(i)}                     end
def repl(st,en,n=1);       st.step(en,n){|i|yield(i)}                 end

class Node
  attr_accessor :id, :edges, :cost, :done, :from
  def initialize(id, edges=[], cost=nil, done=false)
    @id, @edges, @cost, @done = id, edges, cost, done
  end
end
class Edge
  attr_reader :cost, :nid
  def initialize(cost, nid)
    @cost, @nid = cost, nid
  end
end
class Graph
  def initialize(data)
    @nodes =
      data.map do |id, edges|
        edges.map! { |edge| Edge.new(*edge) }
        Node.new(id, edges)
      end
  end
end

class Graph
  def cost(nid, sid)
    dijkstra(sid)
    @nodes.find { |node| node.id == nid }.cost
  end
end

class Graph
  private
  def dijkstra(sid)
    @nodes.each do |node|
      node.cost = node.id == sid ? 0 : nil
      node.done = false
      node.from = nil
    end
    loop do
      done_node = nil
      @nodes.each do |node|
        next if node.done or node.cost.nil?
        done_node = node if done_node.nil? or node.cost < done_node.cost
      end
      break unless done_node
      done_node.done = true
      done_node.edges.each do |edge|
        to = @nodes.find{ |node| node.id == edge.nid }
        cost = done_node.cost + edge.cost
        from = done_node.id
        if to.cost.nil? || cost >= to.cost
          to.cost = cost
          to.from = from
        end
      end
    end
  end
end

n,m = gi
l  =  Hash.new

rep m do
  a,b,c = gi
  if l[a.to_s] == nil
    l[a.to_s] = []
  end
  if l[b.to_s] == nil
    l[b.to_s] = []
  end
  l[a.to_s] << [c,b.to_s]
  l[b.to_s] << [c,a.to_s]
end
g = Graph.new l
if g.cost 1.to_s,1.to_s != 0
  puts "inf"
else
puts g.cost(1.to_s,n.to_s)
end