Problem: Dima came to the horse land. There are n horses living in the land. Each horse in the horse land has several enemies (enmity is a symmetric relationship). The horse land isn't very hostile, so the number of enemies of each horse is at most 3.

Right now the horse land is going through an election campaign. So the horses trusted Dima to split them into two parts. At that the horses want the following condition to hold: a horse shouldn't have more than one enemy in its party.

Help Dima split the horses into parties. Note that one of the parties can turn out to be empty.

Input

The first line contains two integers n, m <image> — the number of horses in the horse land and the number of enemy pairs.

Next m lines define the enemy pairs. The i-th line contains integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi), which mean that horse ai is the enemy of horse bi.

Consider the horses indexed in some way from 1 to n. It is guaranteed that each horse has at most three enemies. No pair of enemies occurs more than once in the input.

Output

Print a line, consisting of n characters: the i-th character of the line must equal "0", if the horse number i needs to go to the first party, otherwise this character should equal "1".

If there isn't a way to divide the horses as required, print -1.

Examples

Input

3 3
1 2
3 2
3 1


Output

100


Input

2 1
2 1


Output

00


Input

10 6
1 2
1 3
1 4
2 3
2 4
3 4


Output

0110000000

Solution (in JAVA):

Solution:


import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class DimaAndHorses {
	static int[] locHorse;
	static List<List<Integer>> enemies;
	public static void main(String[] args){
		FastScanner sc= new FastScanner();
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		
		//enemies[i] = list of enemies of horse i
		enemies = new ArrayList<List<Integer>>();
		for(int horse=0;horse<=n;horse++){
			enemies.add(new ArrayList<Integer>());
		}
		
		for(int i=1;i<=m;i++){
			int h1 = sc.nextInt();
			int h2 = sc.nextInt();
			enemies.get(h1).add(h2);
			enemies.get(h2).add(h1);
		}
		
		//all horse in group 0 initially
		locHorse = new int[n+1];
		for(int horse=1;horse<=n;horse++){
			jump(horse);
		}
		for(int horse=1;horse<=n;horse++){
			System.out.print(locHorse[horse]);
		}
	}
	
	public static void jump(int horse){
		int countEnemy = 0;
		for(Integer enemy : enemies.get(horse)){
			if(locHorse[enemy] == locHorse[horse]){
				countEnemy++;
			}
		}
		if(countEnemy >= 2){
			locHorse[horse] = locHorse[horse] == 0 ? 1 : 0;
			for(Integer enemy : enemies.get(horse)){
				if(locHorse[enemy] == locHorse[horse]){
					jump(enemy);
				}
			}
		}
	}

	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}
}