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

Example Output

5 2 1 2