Problem: Vitaly has an array of n distinct integers. Vitaly wants to divide this array into three non-empty sets so as the following conditions hold: 

  1. The product of all numbers in the first set is less than zero ( < 0). 
  2. The product of all numbers in the second set is greater than zero ( > 0). 
  3. The product of all numbers in the third set is equal to zero. 
  4. Each number from the initial array must occur in exactly one set. 



Help Vitaly. Divide the given array.

Input

The first line of the input contains integer n (3 ≤ n ≤ 100). The second line contains n space-separated distinct integers a1, a2, ..., an (|ai| ≤ 103) — the array elements.

Output

In the first line print integer n1 (n1 > 0) — the number of elements in the first set. Then print n1 numbers — the elements that got to the first set.

In the next line print integer n2 (n2 > 0) — the number of elements in the second set. Then print n2 numbers — the elements that got to the second set.

In the next line print integer n3 (n3 > 0) — the number of elements in the third set. Then print n3 numbers — the elements that got to the third set.

The printed sets must meet the described conditions. It is guaranteed that the solution exists. If there are several solutions, you are allowed to print any of them.

Examples

Input

3
-1 2 0


Output

1 -1
1 2
1 0


Input

4
-1 -2 -3 0


Output

1 -1
2 -3 -2
1 0

Solution (in JAVA):

Solution:
//package HackerEarthA;
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.text.*;
import java.math.*;
import java.util.regex.*;




/**
 *
 * @author prabhat
 */
public class  easy18{
   public  static long[] BIT;
   public  static long[] tree;
  
   public  static long[] sum;
   public  static int mod=1000000007;
   public  static int[][] dp;
   public  static boolean[][] isPalin;
   public  static int max1=1000005;
   public  static int[][] g;
   public  static LinkedList<Pair> l[];
   public  static int n,m,q,k,t,arr[],b[],cnt[],chosen[],pos[],ans;
   public  static ArrayList<Integer> adj[],al;
   public  static TreeSet<Integer> ts;
   public  static   char[][] s;
   public  static int depth,mini,maxi;
   public  static long V[],low,high,min=Long.MAX_VALUE;
   public  static boolean visit[][],isPrime[],used[];
   public  static int[][] dist;
   public  static ArrayList<Integer>prime;
   public static int[] x={0,1};
   public static int[] y={-1,0};
   public  static ArrayList<Integer> divisor[]=new ArrayList[1500005];
   public  static  int[][] subtree,parent,mat;
   public  static  TreeMap<Integer,Integer> tm;
   public  static LongPoint[] p;
   public  static int[][] grid;
   public  static ArrayList<Pair> list;
   public static TrieNode root;
  static  LinkedHashMap<String,Integer> map;
   public static BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
   public  static void main(String[] args) throws Exception
   {
   	   InputReader in = new InputReader(System.in);
	   PrintWriter pw=new PrintWriter(System.out);
	   n=in.ii();
	   arr=in.iia(n);
	   ArrayList<Integer> pos=new ArrayList<>();
	   ArrayList<Integer> neg=new ArrayList<>();
	   ArrayList<Integer> zero=new ArrayList<>();
	   for(int i:arr)
	   {
		   if(i>0)pos.add(i);
		   else if(i<0)neg.add(i);
		   else zero.add(i);
	   }
	   if(neg.size()%2==1)
	   {
		   pw.print(1+" "+neg.get(0));
		   pw.println();
		   int u=neg.size()-1;
		   int v=pos.size();
		   pw.print(u+v+" ");
		   for(int i=1;i<neg.size();i++)pw.print(neg.get(i)+" ");
		   for(int i:pos)pw.print(i+" ");
		   pw.println();
		   pw.print(zero.size()+" ");
		   for(int i:zero)pw.print(i+" ");

	   }
	   else{
		pw.print(1+" "+neg.get(0));
		pw.println();
		int u=neg.size()-2;
		int v=pos.size();
		pw.print(u+v+" ");
		for(int i=2;i<neg.size();i++)pw.print(neg.get(i)+" ");
		for(int i:pos)pw.print(i+" ");
        pw.println();
		pw.print(zero.size()+1+" ");
		for(int i:zero)pw.print(i+" ");
	
		pw.print(neg.get(1));
		pw.println();
		
	   }

	pw.close();
   
}

public static void dfs1(int cur)
{
	used[cur]=true;
	cnt[cur]=1;
	for(int ver:adj[cur])
	{
		if(used[ver])continue;
		dfs1(ver);
        cnt[cur]+=cnt[ver];
	}
}
static ArrayList<String> dfs(String s,String[] sarr,HashMap<String, ArrayList<String>> map)
{
   if(map.containsKey(s))return map.get(s);
   ArrayList<String> res=new ArrayList<>();
   if(s.length()==0)
   {
	   res.add("");
	   return res;
   }

   for(String word:sarr)
   {
	   if(s.startsWith(word))
	   {
		   ArrayList<String > sub=dfs(s.substring(word.length()),sarr,map);
		   for(String s2:sub)
		   {
			   res.add(word+ (s2.isEmpty() ? "" : " ")+s2);
		   }
	   }
   }
   map.put(s,res);
   return res;
}
static class SegmentTree{
  
  int n;
  int max_bound;
 
  public SegmentTree(int n)
  {
	
	  this.n=n;
	  tree=new long[4*n+1];
	  build(1,0,n-1);
  }
void build(int c,int s,int e)
{
   if(s==e)
   {
	   tree[c]=arr[s];
	   return ;
   }

   int mid=(s+e)>>1;
   build(2*c,s,mid);
   build(2*c+1,mid+1,e);
   tree[c]=(tree[2*c]+tree[2*c+1]);
}
void put(int c,int s, int e,int l,int r,int  v) {
	if(l>e||r<s||s>e)return ;
	if (s == e) 
	{
		tree[c] = arr[s]^v;
		return;
	}
	int mid = (s + e) >> 1;
	if (l>mid) put(2*c+1,m+1, e , l,r, v);
	else if(r<=mid)put(2*c,s,m,l,r , v);
	else{
      
	}
	
}
long query(int c,int s,int e,int l,int r)
{
   if(e<l||s>r)return 0L;

   if(s>=l&&e<=r)
   {
	return tree[c];
   }

	int mid=(s+e)>>1;

	return (query(2*c,s,mid,l,r)+query(2*c+1,mid+1,e,l,r));
 }
}  
  
static void update(int indx,long val)
   {
	   while(indx<max1)
	   {
		   BIT[indx]+=val;
		   indx+=(indx&(-indx));
	   }
	   
   }
static long query1(int indx)
   {
	   long sum=0;
	   while(indx>0)
	   {
		   sum+=BIT[indx];
		 //  System.out.println(indx);
		   indx-=(indx&(-indx));
	   }
	   return sum;
	}
   
   
   public static ListNode removeNthFromEnd(ListNode a, int b) {
       
    int cnt=0;
	ListNode ra1=a;
	ListNode ra2=a;
	while(ra1!=null){ra1=ra1.next; cnt++;}
	
	if(b>cnt)return a.next;
	else if(b==1&&cnt==1)return null;
	else{
		int y=cnt-b+1;
		int u=0;
		ListNode prev=null;
		while(a!=null)
		{
			u++;
		   if(u==y)
		   {
			   if(a.next==null)prev.next=null;
			   else
			   {
				   if(prev==null)return ra2.next;
				   prev.next=a.next;
				   a.next=null;
			   }
			   break;
		   }
		   prev=a;
		   a=a.next;
		}
	}
	return ra2;
}
   static ListNode rev(ListNode a)
   {
       ListNode prev=null;
       ListNode cur=a;
       ListNode next=null;
       while(cur!=null)
       {
           next=cur.next;
           cur.next=prev;
           prev=cur;
           cur=next;
       }
       return prev;
   }
  
  static class ListNode {
	     public int val;
	     public ListNode next;
	     ListNode(int x) { val = x; next = null; }
	 }
   static class TrieNode
   {
	   int value;  // Only used in leaf nodes
	   TrieNode[] arr =  new TrieNode[2];
	   public TrieNode() {
		   value = 0;
		   arr[0] = null;
		   arr[1] = null;
	   }
   }
   static void insert(int pre_xor)
   {
	   TrieNode temp = root;
	   
	   // Start from the msb, insert all bits of
	   // pre_xor into Trie
	   for (int i=31; i>=0; i--)
	   {
		   // Find current bit in given prefix
		   int val = (pre_xor & (1<<i)) >=1 ? 1 : 0;
		   
		   // Create a new node if needed
		   if (temp.arr[val] == null)
			   temp.arr[val] = new TrieNode();
		   
		   temp = temp.arr[val];
	   }
	 
	   // Store value at leaf node
	   temp.value = pre_xor;
   }
   
   static int query(int pre_xor)
   {
	   TrieNode temp = root;
	   for (int i=31; i>=0; i--)
	   {
		   // Find current bit in given prefix
		   int val = (pre_xor & (1<<i)) >= 1 ? 1 : 0;
	 
		   // Traverse Trie, first look for a
		   // prefix that has opposite bit
		   if (temp.arr[val] != null)
			   temp = temp.arr[val];
	 
		   // If there is no prefix with opposite
		   // bit, then look for same bit.
		   else if (temp.arr[1-val] != null)
			   temp = temp.arr[1-val];
	   }
	   return pre_xor^(temp.value);
   }
 
   public static String add(String s1,String s2)
   {
	   int n=s1.length()-1;
	   int m=s2.length()-1;
	   int rem=0;
	   int carry=0;
	   int i=n;
	   int j=m;
	   String ans="";
	   while(i>=0&&j>=0)
	   {
		 int c1=(int)(s1.charAt(i)-'0');
		 int c2=(int)(s2.charAt(j)-'0');
		 int sum=c1+c2;
		 sum+=carry;
		 rem=sum%10;
		 carry=sum/10;
         ans=rem+ans;
		  i--; j--;
		  
	   }
	   while(i>=0)
	   {
		int c1=(int)(s1.charAt(i)-'0');
	
		int sum=c1;
		sum+=carry;
		rem=sum%10;
		carry=sum/10;
		ans=rem+ans;
		i--;
	   }
	   while(j>=0)
	   {
	
		int c2=(int)(s2.charAt(j)-'0');
		int sum=c2;
		sum+=carry;
		rem=sum%10;
		carry=sum/10;
		ans=rem+ans;
		j--;
	   }

	   if(carry>0)ans=carry+ans;
	   return ans;
   }
   public static String[] multiply(String A, String B) {
	int lb=B.length();
	char[] a=A.toCharArray();
	char[] b=B.toCharArray();
	String[] s=new String[lb];
	int cnt=0;
	int y=0;
	String s1="";
q=0;
	for(int i=b.length-1;i>=0;i--)
	{
		int rem=0;
		int carry=0;
		
	
		for(int j=a.length-1;j>=0;j--)
		{
			int mul=(int)(b[i]-'0')*(int)(a[j]-'0');
			mul+=carry;
			rem=mul%10;
			carry=mul/10;
			s1=rem+s1;
		}
		s1=carry+s1;
		s[y++]=s1;
		q=Math.max(q,s1.length());
		s1="";
		for(int i1=0;i1<y;i1++)s1+='0';
		
	}
	return s;
}
   public static long nCr(long total, long choose)
   {
	   if(total < choose)
		   return 0;
	   if(choose == 0 || choose == total)
		   return 1;
	   return nCr(total-1,choose-1)+nCr(total-1,choose);
   }
 
 
 
   static int get(long s)
   {
	  int ans=0;
	  for(int i=0;i<n;i++)
	  {
		  if(p[i].x<=s&&s<=p[i].y)ans++;
	  }
	  return ans;
   }
   static class LongPoint {
	public long x;
	public long y;

	public LongPoint(long x, long y) {
		this.x = x;
		this.y = y;
	}

	public LongPoint subtract(LongPoint o) {
		return new LongPoint(x - o.x, y - o.y);
	}

	public long cross(LongPoint o) {
		return x * o.y - y * o.x;
	}

}
    static int CountPs(String s,int n)
       {
    	boolean b=false;
    	     char[] S=s.toCharArray();
	       int[][] dp=new int[n][n];
	       boolean[][] p=new boolean[n][n];
	       for(int i=0;i<n;i++)p[i][i]=true;
	     
	       for(int i=0;i<n-1;i++)
	       {
	    	   if(S[i]==S[i+1])
	    	   {
	    		p[i][i+1]=true;
	    		dp[i][i+1]=0;
	    		b=true;
	    	   }
	       }
	    
	       for(int gap=2;gap<n;gap++)
	       {
	    	   for(int i=0;i<n-gap;i++)
	    	   {
	    		   int j=gap+i;
	    		   if(S[i]==S[j]&&p[i+1][j-1]){p[i][j]=true;}
	    		  
	    		  if(p[i][j])
	    			   dp[i][j]=dp[i][j-1]+dp[i+1][j]+1-dp[i+1][j-1];
	    		   
	    		   else if(!p[i][j]) dp[i][j]=dp[i][j-1]+dp[i+1][j]-dp[i+1][j-1];
	    		  
	    		   //if(dp[i][j]>=1)
                             //  return true;
	    	   }
	       }
	      
	   // return b; 
    return dp[0][n-1];
	       
    }
  
  
  static void Seive()
  {
      isPrime=new boolean[1500005];
      Arrays.fill(isPrime,true);
	 for(int i=0;i<1500005;i++){divisor[i]=new ArrayList<>();}
	 int u=0;
	 prime=new ArrayList<>();
      for(int i=2;i<=(1500000);i++)
      {
         
          if(isPrime[i])
          {
			prime.add(i);
              for(int j=i;j<1500000;j+=i)
              {
                  
                  divisor[j].add(i);
                  
                  isPrime[j]=false;
              }
         /*    for(long x=(divCeil(low,i))*i;x<=high;x+=i)
             {
                 divisor[(int)(x-low)].add(i*1L);
             }*/
              
          }
      }
      
  }
  static long divCeil(long a,long b)
  {
      return (a+b-1)/b;
  }
  static long root(int pow, long x) {
        long candidate = (long)Math.exp(Math.log(x)/pow);
        candidate = Math.max(1, candidate);
        while (pow(candidate, pow) <= x) {
            candidate++;
        }
        return candidate-1;
    }
    
    static long pow(long x, int pow)
    {
        long result = 1;
        long p = x;
        while (pow > 0) {
            if ((pow&1) == 1) {
                if (result > Long.MAX_VALUE/p) return Long.MAX_VALUE;
                result *= p;
            }
            pow >>>= 1;
            if (pow > 0 && p >= 4294967296L) return Long.MAX_VALUE;
            p *= p;
        }
        return result;
    }
  
  static boolean valid(int i,int j)
  {
	  if(i>=0&&i<n&&j>=0&&j<m)return true;
	  return false;
  }
  private static class DSU{
		int[] parent;
		int[] rank;
		int cnt;
		public DSU(int n){
			parent=new int[n];
			rank=new int[n];
			for(int i=0;i<n;i++){
				parent[i]=i;
				rank[i]=1;
			}
			cnt=n;
		}
		int find(int i){
	        while(parent[i] !=i){
	        	parent[i]=parent[parent[i]];
	        	i=parent[i];
	        }
	        return i;
	    }
		int Union(int x, int y){
	        int xset = find(x);
	        int yset = find(y);
	        if(xset!=yset)
	        	cnt--;
	        if(rank[xset]<rank[yset]){
	        	parent[xset] = yset;
		        rank[yset]+=rank[xset];
		        rank[xset]=0;
		        return yset;
	        }else{
	        	parent[yset]=xset;
	        	rank[xset]+=rank[yset];
	        	rank[yset]=0;
	        	return xset;
	        }
	    }
	}
  public static int[][] packU(int n, int[] from, int[] to, int max) {
	    
	    int[][] g = new int[n][];
	    int[] p = new int[n];
	    for (int i = 0; i < max; i++) p[from[i]]++;
	    for (int i = 0; i < max; i++) p[to[i]]++;
	    for (int i = 0; i < n; i++) g[i] = new int[p[i]];
	    for (int i = 0; i < max; i++) {
	        g[from[i]][--p[from[i]]] = to[i];
	        g[to[i]][--p[to[i]]] = from[i];
	    }
	    return g;
	}
	public static int[][] parents3(int[][] g, int root) {
	    int n = g.length;
	    int[] par = new int[n];
	    Arrays.fill(par, -1);

	    int[] depth = new int[n];
	    depth[0] = 0;

	    int[] q = new int[n];
	    q[0] = root;
	    for (int p = 0, r = 1; p < r; p++) {
	        int cur = q[p];
	        for (int nex : g[cur]) {
	            if (par[cur] != nex) {
	                q[r++] = nex;
	                par[nex] = cur;
	                depth[nex] = depth[cur] + 1;
	            }
	        }
	    }
	    return new int[][]{par, q, depth};
	}
	public static int lower_bound(int[] nums, int target) {
        int low = 0, high = nums.length - 1;
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (nums[mid] < target)
                low = mid + 1;
            else
                high = mid;
        }
        return nums[low] == target ? low : -1;
    }

    public static int upper_bound(int[] nums, int target) {
        int low = 0, high = nums.length - 1;
        while (low < high) {
            int mid = low + (high + 1 - low) / 2;
            if (nums[mid] > target)
                high = mid - 1;
            else
                low = mid;
        }
        return nums[low] == target ? low : -1;
    }
  public static boolean palin(String s)
	{
	   int i=0;
	   int j=s.length()-1;
	   while(i<j)
	   {
		   if(s.charAt(i)==s.charAt(j))
		   {
			   i++;
			   j--;
		   }
		   else return false;     
	   }
	   return true;
	}
	
  
  
  
 

public static int gcd(int a,int b)
{
	int res=1;
	while(a>0)
	{
		res=a;
		a=b%a;
		b=res;
	}
	return res;
}
static int lcm(int a,int b)
{
	return (a*b)/(gcd(a,b));
}

public static long pow(long n,long p,long m)
{
	 long  result = 1;
	  if(p==0)
	    return 1;
	
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    if(result>=m)
	    result%=m;
	    p >>=1;
	    n*=n;
	    if(n>=m)
	    n%=m;
	}
	return result;
}

    /**
     *
     * @param n
     * @param p
     * @return
     */
    public static long pow(long n,long p)
     {
	long  result = 1;
	  if(p==0)
	    return 1;
	if (p==1)
	    return n;
	while(p!=0)
	{
	    if(p%2==1)
	        result *= n;
	    p >>=1;
	    n*=n;
	}
	return result;

     }




static class Edge implements Comparator<Edge> {
	private int u;
	private int v;
	private long w;
	public Edge() {
	}
	public Edge(int u, int v, long w) {
		this.u=u;
		this.v=v;
		this.w=w;
	}
	public int getU() {
		return u;
	}
	public void setU(int u) {
		this.u = u;
	}
	public int getV() {
		return v;
	}
	public void setV(int v) {
		this.v = v;
	}
	public long getW() {
		return w;
	}
	public void setW(int w) {
		this.w = w;
	      }
	public long compareTo(Edge e)
	  {
		return (this.getW() - e.getW());
	}

        @Override
        public int compare(Edge o1, Edge o2) {
            throw new UnsupportedOperationException("Not supported yet."); //To change body of generated methods, choose Tools | Templates.
        }
	
}



static class Pair implements Comparable<Pair>
{
	int x,y;
	Pair (int a,int b)
	{
		this.x=a;
		this.y=b;
	}

	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		if(this.x!=o.x)
		return -Integer.compare(this.x,o.x);
		else
			return -Integer.compare(this.y, o.y);
		//return 0;
	}
	public boolean equals(Object o) {
       if (o instanceof Pair) {
           Pair p = (Pair)o;
           return p.x == x && p.y == y;
       }
       return false;
   }
   public int hashCode() {
       return new Integer(x).hashCode() * 31 + new Integer(y).hashCode();
   }
}

static  class InputReader
{
   private InputStream stream;
   private byte[] buf = new byte[1024];

   private SpaceCharFilter filter;
    byte inbuffer[] = new byte[1024];
   int lenbuffer = 0, ptrbuffer = 0;
    final int M = (int) 1e9 + 7;
   int md=(int)(1e7+1);
    int[] SMP=new int[md];
   final double eps = 1e-6;
   final double pi = Math.PI;

	PrintWriter out;
   String check = "";
 InputStream   obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
   public InputReader(InputStream stream)
   {
       this.stream = stream;
   }

    int readByte() {
	        if (lenbuffer == -1) throw new InputMismatchException();
	        if (ptrbuffer >= lenbuffer) {
	            ptrbuffer = 0;
	            try {
	                lenbuffer = obj.read(inbuffer);
	            } catch (IOException e) {
	                throw new InputMismatchException();
	            }
	        }
	        if (lenbuffer <= 0) return -1;
	        return inbuffer[ptrbuffer++];
   }

   public  int read()
   {
       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;
   }

   String is() {
	        int b = skip();
	        StringBuilder sb = new StringBuilder();
	        while (!(isSpaceChar(b))) // when nextLine, (isSpaceChar(b) && b!=' ')
	        {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
   }
   public   int ii() {
	        int num = 0, b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
 public   long il() {
	        long num = 0;
	        int b;
	        boolean minus = false;
	        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
	        if (b == '-') {
	            minus = true;
	            b = readByte();
	        }
	        while (true) {
	            if (b >= '0' && b <= '9') {
	                num = num * 10 + (b - '0');
	            } else {
	                return minus ? -num : num;
	            }
	            b = readByte();
	        }
   }
   
	    boolean isSpaceChar(int c) {
	        return (!(c >= 33 && c <= 126));
	       }

	      int skip()
	        {
	        int b;
	        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
	        return b;
	        }

	    float nf() {
	        return Float.parseFloat(is());
	    }

	    double id() {
	        return Double.parseDouble(is());
	    }

	    char ic() {
	        return (char) skip();
	    }

	    int[] iia(int n) {
	        int a[] = new int[n];
	        for (int i = 0; i<n; i++) a[i] = ii();
	        return a;
	    }

	    long[] ila(int n) {
	        long a[] = new long[n];
	        for (int i = 0; i <n; i++) a[i] = il();
	        return a;
	    }

	    String[] isa(int n) {
	        String a[] = new String[n];
	        for (int i = 0; i < n; i++) a[i] = is();
	        return a;
	    }


		 long mul(long a, long b) { return a * b % M; }

			long div(long a, long b)
				 {
					return mul(a, pow(b, M - 2));

		           }



	    double[][] idm(int n, int m) {
	        double a[][] = new double[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j < m; j++) a[i][j] = id();
	        return a;
	        }

	    int[][] iim(int n, int m) {
	        int a[][] = new int[n][m];
	        for (int i = 0; i < n; i++) for (int j = 0; j <m; j++) a[i][j] = ii();
	        return a;
          }


   public String readLine() {
       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 interface SpaceCharFilter
   {
       public boolean isSpaceChar(int ch);
   }
   public boolean isEndOfLine(int c) {
       return c == '\n' || c == '\r' || c == -1;
   }
}

}