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 109+7)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 nn and mm: the number of cities and the number of flights. The cities are numbered 1,2,,n1,2,\ldots,n. City 1 is Syrjälä, and city nn is Lehmälä.

After this, there are mm lines describing the flights. Each line has three integers aa, bb, and cc: there is a flight from city aa to city bb with price cc. 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

  • 1n1051 \le n \le 10^5
  • 1m21051 \le m \le 2 \cdot 10^5
  • 1a,bn1 \le a,b \le n
  • 1c1091 \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