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Problems

High Score

High Score

Time limit 1 second
Memory limit 128 MiB

You play a game consisting of n rooms and m tunnels. Your initial score is 0, and each tunnel increases your score by x where x may be both positive or negative. You may go through a tunnel several times.

Your task is to walk from room 1 to room n. What is the maximum score you can get?

Input data

The first line has two integers n\:(1 \le n \le 2500) and m\:(1 \le m \le 5000): the number of rooms and tunnels. The rooms are numbered 1, 2, \dots , n.

Then, there are m lines describing the tunnels. Each line has three integers a, b\:(1 \le a, b \le n) and x\:(−10^9 \le x \le 10^9): the tunnel starts at room a, ends at room b, and it increases your score by x. All tunnels are one-way tunnels.

You can assume that it is possible to get from room 1 to room n.

Output data

Print one integer: the maximum score you can get. However, if you can get an arbitrarily large score, print -1.

Examples

Input example #1
4 5
1 2 3
2 4 -1
1 3 -2
3 4 7
1 4 4
Output example #1
5