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?

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.

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

Print four integers according to the problem statement.