Planets and Kingdoms

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