Problem: Recently, Pari and Arya did some research about NP-Hard problems and they found the minimum vertex cover problem very interesting.

Suppose the graph G is given. Subset A of its vertices is called a vertex cover of this graph, if for each edge uv there is at least one endpoint of it in this set, i.e. <image> or <image> (or both).

Pari and Arya have won a great undirected graph as an award in a team contest. Now they have to split it in two parts, but both of them want their parts of the graph to be a vertex cover.

They have agreed to give you their graph and you need to find two disjoint subsets of its vertices A and B, such that both A and B are vertex cover or claim it's impossible. Each vertex should be given to no more than one of the friends (or you can even keep it for yourself).

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 100 000, 1 ≤ m ≤ 100 000) — the number of vertices and the number of edges in the prize graph, respectively.

Each of the next m lines contains a pair of integers ui and vi (1 ≤ ui, vi ≤ n), denoting an undirected edge between ui and vi. It's guaranteed the graph won't contain any self-loops or multiple edges.

Output

If it's impossible to split the graph between Pari and Arya as they expect, print "-1" (without quotes).

If there are two disjoint sets of vertices, such that both sets are vertex cover, print their descriptions. Each description must contain two lines. The first line contains a single integer k denoting the number of vertices in that vertex cover, and the second line contains k integers — the indices of vertices. Note that because of m ≥ 1, vertex cover cannot be empty.

Examples

Input

4 2
1 2
2 3


Output

1
2 
2
1 3 


Input

3 3
1 2
2 3
1 3


Output

-1

Note

In the first sample, you can give the vertex number 2 to Arya and vertices numbered 1 and 3 to Pari and keep vertex number 4 for yourself (or give it someone, if you wish).

In the second sample, there is no way to satisfy both Pari and Arya.

Solution (in JAVA):

Solution:
import java.io.* ;
import java.util.* ;
public class Codeshefcode {
	final static long r = 1000000007 ;
	static FasterScanner ip = new FasterScanner() ;
	static PrintWriter op = new PrintWriter(System.out) ; 
	public static void main(String[] args) throws IOException{
	    int n = ip.i() ;
	    int m = ip.i() ;
	    MyList[] adj = new MyList[n+1] ;
	    for(int i=0 ; i<=n ; i++)
	    	adj[i] = new MyList() ;
	    for(int i=0 ; i<m ; i++){
	    	int a = ip.i() ;
	    	int b = ip.i() ;
	    	adj[a].add(b) ;
	    	adj[b].add(a) ;	    	
	    }
	    boolean possible = true ;
	    int col[] = new int[n+1] ;
	    for(int i=1 ; i<=n && possible ; i++){
	    	if(col[i]==0 && adj[i].size()!=0){
	    		Queue<pair> Q = new LinkedList<pair>() ;
	    	    Q.add(new pair(i,1)) ;
	    	    while(!Q.isEmpty() && possible){
	    	    	pair p = Q.poll() ;
	    	    	int node = p.x() ;	    	    	
	    	    	int color = p.y() ;
	    	    	col[node]=color ;
	    	    	MyList ngs = adj[node] ;
	    	    	for(int nnode : ngs){
	    	    		if(col[nnode]==0)
	    	    			Q.add(new pair(nnode,3-color)) ;
	    	    		else
	    	    			if(col[nnode]==col[node])
	    	    				possible=false ;
	    	    	}
	    	    }
	    	}
	    }
	    if(possible){
	    	MyList Graph1 = new MyList() ;
	    	MyList Graph2 = new MyList() ;
	    	for(int i=1 ; i<=n ; i++)
	    		if(col[i]==1)
	    			Graph1.add(i) ;
	    		else
	    			if(col[i]==2)
	    			   Graph2.add(i) ;	    	
	    	op.println(Graph1.size()) ;
	    	for(int i : Graph1)
	    		op.print(i+" ") ;
	    	op.println("") ;
	    	op.println(Graph2.size()) ;
	    	for(int i : Graph2)
	    		op.print(i+" ") ;
	    	op.println("") ;
	    }
	    else
	    	op.println(-1) ;  
		Finish() ;
	}	
	static void Finish(){
		op.flush(); 
		op.close();
	}
}
@SuppressWarnings("serial") 
class MyList extends ArrayList<Integer>{
	
}
class pair implements Comparable<pair>{
	private int x ;
	private int y ;
	pair(int a,int b){
		x=a ;
		y=b ;		
	}
	public int x(){
		return x ;
	}
	public int y(){
		return y ;
	}
	public int compareTo(pair p){
		int l = Long.compare(this.x,p.x) ;
		if(l!=0)
			return l ;
		return Long.compare(this.y,p.y) ;
	}
}
class FasterScanner { 
    private InputStream mIs;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars; 
    public FasterScanner() {
        this(System.in);
    } 
    public FasterScanner(InputStream is) {
        mIs = is;
    } 
    public int read() {
        if (numChars == -1) 
            throw new InputMismatchException();    
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = mIs.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0) 
                return -1;            
        }
        return buf[curChar++];
    } 
    public String nextLine() {
        int c = read();
        while (isSpaceChar(c)) 
            c = read();        
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    } 
    public String S() {
        int c = read();
        while (isSpaceChar(c)) 
            c = read();        
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        }while (!isSpaceChar(c));
        return res.toString();
    } 
    public long l() {
        int c = read();
        while (isSpaceChar(c)) 
            c = read();        
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do{
           if (c < '0' || c > '9') 
               throw new InputMismatchException();            
           res *= 10;
           res += c - '0';
           c = read();
        }while(!isSpaceChar(c));
        return res * sgn;
    } 
    public int i() {
        int c = read();
        while (isSpaceChar(c))
            c = read();        
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do{
            if (c < '0' || c > '9') 
                throw new InputMismatchException();            
            res *= 10;
            res += c - '0';
            c = read();
        }while (!isSpaceChar(c));
        return res * sgn;
    } 
    public boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    } 
    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    } 
}