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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

{-# LANGUAGE FlexibleContexts #-}

import Control.Monad
import Data.STRef
import Data.Array.MArray
import Data.Array.Unboxed
import Data.Array.ST
import Control.Monad.ST
{--
data Score = Inf | Fin Int deriving (Eq,Show)
instance Ord Score where
  compare Inf     Inf = EQ
  compare (Fin _) Inf = LT
  compare Inf (Fin _) = GT
  compare (Fin a) (Fin b)= compare a b

plus::Score -> Score -> Score
plus Inf _ = Inf
plus _ Inf = Inf
plus (Fin a) (Fin b) = Fin (a+b)

--type W_D_graph = Array (Int,Int) Score
--graph implimentation changed: (a,b,c):a to b wieght c
--}
type Graph = [(Int,Int,Int)]



bellman_ford::Graph -> Int -> Int -> UArray Int Int
bellman_ford gr size st = runSTUArray $ do
  tab<- newArray (1,size) maxBound
  writeArray tab st 0
  flag_tab<- newArray (1,size) True
  flagptr<-newSTRef flag_tab
  tab_ptr<-newSTRef tab
  gr_ptr <-newSTRef gr
  forM_ [1..(size-1)] (propagate gr_ptr tab_ptr)
  forM_ [1..size    ] (propagate' gr_ptr tab_ptr flagptr)
  forM_ [1..size    ] (rewrite tab_ptr flagptr)
  return tab
      where rewrite tab_ptr flagptr i = do
                                        tab<-readSTRef tab_ptr
                                        flags<-readSTRef flagptr
                                        i_res<-readArray tab i
                                        i_flag<-readArray flags i
                                        writeArray tab i (if i_flag then i_res else minBound)

{--
  ar<-freeze tab
  let result =listArray (1,size) $(map (\(x,b)->if b then Just x else Nothing) (elems ar))
  return result
--}

propagate::STRef s Graph ->STRef s (STUArray s Int Int)  -> Int -> (ST s ())
propagate gr_ptr tab_ptr _= do
  gr<-readSTRef gr_ptr
  forM_ gr one_edge_update
        where one_edge_update (a,b,c) = do
                              tab<-readSTRef tab_ptr
                              tab_a<-readArray tab a
                              tab_b<-readArray tab b
                              let next_b = min (tab_a+c) tab_b
                              writeArray tab b next_b

propagate'::STRef s Graph ->STRef s (STUArray s Int Int) -> STRef s (STUArray s Int Bool) -> Int -> (ST s ())
propagate' gr_ptr tab_ptr flagptr _= do
  gr<-readSTRef gr_ptr
  forM_ gr one_edge_update
        where one_edge_update (a,b,c) = do
                              tab<-readSTRef tab_ptr
                              tab_a<-readArray tab a
                              tab_b<-readArray tab b
                              let next_b = min (tab_a+c) tab_b
                              let next_flag = (next_b == tab_b)
                              writeArray tab b next_b
                              flags<-readSTRef flagptr
                              writeArray flags b next_flag


n_get::Int ->IO [(Int,Int,Int)]
n_get 0 =return []
n_get n =do
  d<-getLine
  let a:b:w:[]= map read (words d)
  rest <- n_get (n-1)
  return ((a,b,(-w)):rest)

main::IO()
main=do
  nmc<-getLine
  let n:m:[]=map read (words nmc)::[Int]
  gr<-n_get m
  let ans = (bellman_ford gr n 1)!n
  if ans==minBound then do putStr ("inf"++"\n")
                   else do print (-ans)