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