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

You can use each teleporter at most once during the game. How many days can you play if you choose your routes optimally?

**Input**

The first input line has two integers $n$ and $m$: the number of rooms and teleporters. The rooms are numbered $1,2,\dots,n$.

After this, there are $m$ lines describing the teleporters. Each line has two integers $a$ and $b$: there is a teleporter from room $a$ to room $b$.

There are no two teleporters whose starting and ending room are the same.

**Output**

First print an integer $k$: the maximum number of days you can play the game. Then, print $k$ route descriptions according to the example. You can print any valid solution.

**Constraints**

- $2 \le n \le 500$

- $1 \le m \le 1000$

- $1 \le a,b \le n$

**Example**

Input:

`6 7`

1 2

1 3

2 6

3 4

3 5

4 6

5 6

Output:

`2`

3

1 2 6

4

1 3 4 6