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

**Input**

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

After this, there are $m$ lines describing the flights. Each line has two integers $a$ and $b$: there is a flight from city $a$ to city $b$. All flights are one-way flights.

**Output**

First print an integer $k$: the required number of new flights. After this, print $k$ lines describing the new flights. You can print any valid solution.

**Constraints**

- $1 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

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

**Example**

Input:

`4 5`

1 2

2 3

3 1

1 4

3 4

Output:

`1`

4 2