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

Example Output

2
1 1 1 2 2