**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