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

**Input**

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

After this, there are $m$ lines describing the teleporters. Each line has two integers $a$ and $b$: you can travel from planet $a$ to planet $b$ through a teleporter.

**Output**

First print an integer $k$: the number of kingdoms. After this, print for each planet a kingdom label between $1$ and $k$. 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:

`5 6`

1 2

2 3

3 1

3 4

4 5

5 4

Output:

`2`

1 1 1 2 2