You want to travel from Syrjälä to Lehmälä by plane using a minimum-price route. Which cities will you certainly visit?

Input

The first input line contains two integers $n$ and $m$: the number of cities and the number of flights. The cities are numbered $1,2,\ldots,n$. City 1 is Syrjälä, and city $n$ is Lehmälä.

After this, there are $m$ lines describing the flights. Each line has three integers $a$, $b$, and $c$: there is a flight from city $a$ to city $b$ with price $c$. All flights are one-way flights.

You may assume that there is a route from Syrjälä to Lehmälä.

Output

First print an integer $k$: the number of cities that are certainly in the route. After this, print the $k$ cities sorted in increasing order.

Constraints

• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$
• $1 \le c \le 10^9$

Example

Input:

5 6
1 2 3
1 3 4
2 3 1
2 4 5
3 4 1
4 5 8

Output:

4
1 3 4 5