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 OCaml (4.02.3) (judge verdict: Accepted)

let rec fold_n n f v = if n <= 0 then v else fold_n (n-1) f (f v)
let inf = 10101010101010

let () =
  Scanf.scanf "%d %d" @@ fun n m ->
  let a = Array.init m (fun _ -> Scanf.scanf " %d %d %d" (fun a b c -> a-1,b-1,c)) in

  let reach = begin
    let g = Array.init n (fun _ -> []) in
    a |> Array.iter (fun (u,v,_) -> g.(v) <- u :: g.(v));
    let vis = Array.make n false in
    let rec f u =
      vis.(u) <- true;
      List.iter (fun v -> if not vis.(v) then f v) g.(u)
    in f (n-1);
    vis
  end in

  let sc = Array.make n (-inf) in sc.(0) <- 0;
  let mem = Array.make n false in
  let has_loop = true |> fold_n n (fun upd ->
    if not upd then false else begin
      Array.fill mem 0 n false;
      Array.fold_left (fun b (u,v,c) ->
        let b' = sc.(u) + c > sc.(v) in
        if b' then (mem.(v) <- true; sc.(v) <- sc.(u) + c);
        b || b'
        ) false a
    end)
  in
  let inf_loop = has_loop && begin
    Array.init n (fun i -> reach.(i) && mem.(i)) |> Array.fold_left (||) false
  end in

  if inf_loop then
    print_endline "inf"
  else
    Printf.printf "%d\n" sc.(n-1)