Investigation

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