**Time limit:**1.00 s**Memory limit:**512 MB

**Input**

The first input line has two integers $n$ and $m$: the number of cities and flight connections. The cities are numbered $1,2,\ldots,n$. City 1 is Syrjälä, and city $n$ is Metsälä.

After this there are $m$ lines describing the flights. Each line has three integers $a$, $b$, and $c$: a flight begins at city $a$, ends at city $b$, and its price is $c$. Each flight is unidirectional.

You can assume that it is always possible to get from Syrjälä to Metsälä.

**Output**

Print one integer: the price of the cheapest route from Syrjälä to Metsälä.

When you use the discount coupon for a flight whose price is $x$, its price becomes $\lfloor x/2 \rfloor$ (it is rounded down to an integer).

**Constraints**

- $2 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

- $1 \le a,b \le n$

- $1 \le c \le 10^9$

**Example**

Input:

`3 4`

1 2 3

2 3 1

1 3 7

2 1 5

Output:

`2`