**Time limit:**1.00 s**Memory limit:**512 MB

- 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`