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)

import qualified Data.IntMap as M
import Data.Maybe (fromJust)
import Control.Monad
import Data.Array.IO
import Data.List

main = do
  [n, m] <- map read . words <$> getLine :: IO [Int]
  input <- (\[x, y, z] -> zip3 x y z) . transpose . map (map read . words) . lines <$> getContents :: IO [(Int, Int, Int)]
  weight <- newArray (0, n) 0 :: IO (IOUArray Int Int)
  mark <- newArray (1, n) False :: IO (IOUArray Int Bool)
  let graph = foldl makeGraph M.empty input
      neighbor = M.toList . fromJust $ M.lookup 1 graph
  writeArray mark 1 True
  foldM (search graph weight 1 n) mark neighbor
  inf <- readArray weight 0
  ans <- readArray weight n
  if inf == -1 then putStrLn "inf"
               else print ans

type Weight = Int
type Vertex = (Int, Weight)
--key:頂点番号, value:隣接点集合
type Graph = M.IntMap Neighbor
--key:ある点の隣接点の頂点番号, value:辺の重さ
type Neighbor = M.IntMap Weight

--隣接リスト
makeGraph :: Graph -> (Int, Int, Int) -> Graph
makeGraph graph (x, y, z) =
  let nX = M.lookup x graph
  in if nX == Nothing
       then M.insert x (addNeighbor (y, z) M.empty) graph
       else M.insert x (addNeighbor (y, z) $ fromJust nX) graph

addNeighbor :: (Int, Int) -> Neighbor -> Neighbor
addNeighbor (i, weight) ne = M.insert i weight ne

--DFS : 前pre 現在i
search :: Graph -> IOUArray Int Int -> Int -> Int -> IOUArray Int Bool -> Vertex -> IO (IOUArray Int Bool)
search graph weight pre dst mark (i, w) = do
  isMark <- readArray mark i
  case isMark of
    True -> do
      if i == dst
        then do
          wBest <- readArray weight i
          wSum <- readArray weight pre
          writeArray weight i $ max (wSum + w) wBest
          let ne = M.lookup i graph
          if ne == Nothing
            then return mark
            else do
              let neList = M.toList . fromJust $ ne
              return =<< foldM (search graph weight i dst) mark neList
        else do
          writeArray weight 0 (-1)
          return mark
    False -> do
      writeArray mark i True
      wSum <- readArray weight pre
      writeArray weight i (wSum + w)
      let ne = M.lookup i graph
      if ne == Nothing
        then return mark
        else do
          let neList = M.toList . fromJust $ ne
          return =<< foldM (search graph weight i dst) mark neList