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 RankNTypes #-}
import Control.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as MV
import Control.Monad.ST

main :: IO ()
main = readLine >>= main'
    where
        main' [n, m] = readContents m >>= printRes . solve n
        printRes = maybe (putStrLn "inf") print

solve :: Int -> [[Int]] -> Maybe Int
solve n abcs = bellmanFord (n - 1) graph 0 (n - 1) >>= next . edit
    where
        next res = bellmanFord (2 * n - 1) graph 0 (n - 1) >>= check res . edit
        check a b
            | a == b = return a
            | otherwise = Nothing
        edit = negate . fst
        graph = Graph n es inf
        es = map mf abcs
        mf [a, b, c] = Edge (a - 1) (b - 1) (-c)
        inf = 10 ^ 12 + 1

data Graph a = Graph Int [Edge a] a
data Edge a = Edge Int Int a

bellmanFord :: (Ord a, Num a) => Int -> Graph a -> Int -> Int -> Maybe (a, [Int])
bellmanFord m gr@(Graph n es inf) s t = runST (initialize inf >>= loop inf m es)
    where
        initialize :: (Ord a, Num a) => forall s. a -> ST s (MV.STVector s (a, Int))
        initialize inf = MV.replicate n (inf, n) >>= write
            where
                write ds = ds <$ MV.unsafeWrite ds s (fromInteger 0, s)

        loop :: (Ord a, Num a) => forall s. a -> Int -> [Edge a] -> MV.STVector s (a, Int) -> ST s (Maybe (a, [Int]))
        loop inf c es ds = foldM ff False es >>= check
            where
                ff acc (Edge a b c) = rds >>= edit
                    where
                        rds = (,) <$> rf a <*> rf b
                        rf i = fst <$> MV.unsafeRead ds i
                        edit (al, bl)
                            | al >= inf = return acc 
                            | bl > al + c = True <$ (MV.unsafeWrite ds b (al + c, a))
                            | otherwise = return acc 
                check acc 
                    | acc && c > 0 = loop inf (c - 1) es ds 
                    | acc = return Nothing
                    | otherwise = return . calcResult <$> V.unsafeFreeze ds

        calcResult :: V.Vector (a, Int) -> (a, [Int])
        calcResult ds = (fst $ ds V.! t, ploop [] t)
            where
                ploop ps v 
                    | v == s = s : ps
                    | otherwise = ploop (v : ps) . snd $ ds V.! v

readLine :: IO [Int]
readLine = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine