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:
/*
 * The MIT License
 *
 * Copyright 2016 Mouad NACIRI <mouadnaciri1@gmail.com>.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintStream;
import java.util.*;

/**
 *
 * @author NACIRI Mouad <mouadnaciri1@gmail.com>
 * @version 1.5.2
 */

public class CF {
    /* VIP, DON'T TOUCH!! */
    static StringTokenizer ST;
    static BufferedReader IN;
    static PrintStream o, e;
    static {
        IN = new BufferedReader(new InputStreamReader(System.in));
        o = System.out;
        e = System.err;
    }
    /*
    int   2_147_483_647               /  -2_147_483_648
    long  9_223_372_036_854_775_807L  /  -9_223_372_036_854_775_808L
    */
    static ArrayList<Integer>[] g;
    static int[] c;
    public static void main(String[] ag) throws IOException {
        int n = ni(), m = ni();
        ArrayList<Integer>[] r = new ArrayList[2];
        r[0] = new ArrayList<Integer>();
        r[1] = new ArrayList<Integer>();
        g = new ArrayList[n + 1];
        c = new int[ n + 1 ];
        
        for(int i = 0; i < n; i++) { g[i] = new ArrayList<Integer>(); }
        for(int i = 0; i < m; i++) {
            int u = ni() - 1, v = ni() - 1;
            g[u].add(v);
            g[v].add(u);
        }
        
        dfs(0);
        for(int i = 0; i < n; i++) {
            if(c[i] == 0) {
                dfs(i);
            }
        }
        for(int i = 0; i < n; i++) {
            if(c[i] != 0)
                r[c[i] - 1].add(i + 1);
        }
        for(int k = 0; k < 2; k++) {
            o.println(r[k].size());
            for(int i : r[k]) {
                o.print(i);o.print(' ');
            }
            o.println();
        }
        
        cAll();
    }
    
    static void dfs(int u) {
        for(int v : g[u]) {
            if(c[v] == 0) {
                c[v] = (c[u] == 1) ? 2 : 1;
                dfs(v);
            }
            if(c[v] == c[u]) {
                o.println("-1");
                System.exit(0);
            }
        }
    }
    
    //IO stuff...   
    static void ll() { ST = new StringTokenizer(nlnt()); }
    static void ll(String del) { ST = new StringTokenizer(nlnt(), del); }
    static void ll(String s, String del) { ST = new StringTokenizer(s, del); }
    static void lll(String s) { ST = new StringTokenizer(s); }
    
    static int tlen() { return ST == null ? 0 : ST.countTokens(); }
    static boolean hn() { return ST != null && ST.hasMoreTokens(); }
    static String n() {
        if(!hn()) { ll(); }
        return ST.nextToken();
    }
    static String nln() {
        String l = null;
        try {
            while((l = IN.readLine()) != null && l.trim().length() == 0) {}
        } catch(IOException e) { }
        ST = null;
        return l;
    }
    static String nlnt() {
        String l = null;
        try {
            while((l = IN.readLine()) != null && (l = l.trim()).length() == 0) {}
        } catch(IOException e) { }
        ST = null;
        return l;
    }
    static boolean nbl() { return Boolean.parseBoolean(n()); }
    static byte nb() { return Byte.parseByte(n()); }
    static byte nb(int radix) { return Byte.parseByte(n(), radix); }
    static double nd() { return Double.parseDouble(n()); }
    static float nf() { return Float.parseFloat(n()); }
    static int ni() { return Integer.parseInt(n()); }
    static int ni(int radix) { return Integer.parseInt(n(), radix); }
    static long nl() { return Long.parseLong(n()); }
    static long nl(int radix) { return Long.parseLong(n(), radix); }
    static short ns() { return Short.parseShort(n()); }
    static short ns(int radix) { return Short.parseShort(n(), radix); }
    
    static void cAll() throws IOException { IN.close(); }
}