CSES - High Score
• Time limit: 1.00 s
• Memory limit: 512 MB
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

The first input line has two integers $n$ and $m$: 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 $a$, $b$ and $x$: 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

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

Constraints
• $1 \le 2500 \le n$
• $1 \le 5000 \le m$
• $1 \le a,b \le n$
• $-10^9 \le x \le 10^9$
Example

Input:
4 5 1 2 3 2 4 -1 1 3 -2 3 4 7 1 4 4

Output:
5