Planets and Kingdoms

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

A game has $n$ planets, connected by $m$ teleporters. Two planets $a$ and $b$ belong to the same kingdom exactly when there is a route both from $a$ to $b$ and from $b$ to $a$. Your task is to determine for each planet its kingdom.

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