Consider a network consisting of $n$ computers and $m$ connections. Each connection specifies how fast a computer can send data to another computer.

Kotivalo wants to download some data from a server. What is the maximum speed he can do this, using the connections in the network?

Input

The first input line has two integers $n$ and $m$: the number of computers and connections. The computers are numbered $1,2,\dots,n$. Computer $1$ is the server and computer $n$ is Kotivalo's computer.

After this, there are $m$ lines describing the connections. Each line has three integers $a$, $b$ and $c$: computer $a$ can send data to computer $b$ at speed $c$.

Output

Print one integer: the maximum speed Kotivalo can download data.

Constraints

• $1 \le n \le 500$
• $1 \le m \le 1000$
• $1 \le a,b \le n$
• $1 \le c \le 10^9$

Example

Input:

4 5
1 2 3
2 4 2
1 3 4
3 4 5
4 1 3

Output:

6