CSES - Investigation
• Time limit: 1.00 s
• Memory limit: 512 MB

You are going to travel from Syrjälä to Lehmälä by plane. You would like to find answers to the following questions:

• what is the minimum price of such a route?
• how many minimum-price routes are there? (modulo 10^9+7)
• what is the minimum number of flights in a minimum-price route?
• what is the maximum number of flights in a minimum-price route?

# 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

Print four integers according to the problem statement.

# 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:

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


Output:

5 2 1 2