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:
import java.io.*;
import java.util.*;



public class Ladder {
    public static void main(String[] args) throws IOException {
        //BufferedReader reader=new BufferedReader(new FileReader("input.txt"));
        //PrintWriter pw=new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
        //BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        //Scanner scanner=new Scanner(System.in);
        PrintWriter pw=new PrintWriter(System.out);
        Reader scanner = new Reader();

        int n=scanner.nextInt();
        Set<Integer> a=new HashSet<>();
        ArrayList<Integer> neg=new ArrayList<>();
        ArrayList<Integer> pos=new ArrayList<>();
        for (int i = 0; i <n ; i++) {
            a.add(scanner.nextInt());
        }
        for (int t:a) {
            if (t<0)
                neg.add(t);
            else if (t>0)
                pos.add(t);
        }

        pw.println(1+" "+neg.remove(0));
        if (neg.size()%2==0){
            pw.print(pos.size()+neg.size()+" ");
            for (int i = 0; i <pos.size() ; i++) {
                pw.print(pos.get(i)+" ");
            }
            for (int i = 0; i <neg.size() ; i++) {
                pw.print(neg.get(i)+" ");
            }
            pw.println();
            pw.print(1+" "+0+" ");

        }
        else {
            if (pos.size()==0){
                pw.print(2+" "+neg.remove(0)+" "+neg.remove(0));
            }
            else {
                pw.print(pos.size()+" ");
                for (int i = 0; i <pos.size() ; i++) {
                    pw.print(pos.get(i)+" ");
                }
            }
            pw.println();
            pw.print(1+neg.size()+" "+0+" ");
            for (int i = 0; i <neg.size() ; i++) {
                pw.print(neg.get(i)+" ");
            }
        }



        pw.close();

    }


}
/*
class tuple implements Comparable<tuple>{
    int a;
    int b;

    public tuple(int a, int b) {
        this.a = a;
        this.b = b;
    }

    @Override
    public int compareTo(tuple o) {
        return this.a-o.a;
    }
}

*/
class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64];
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') break;
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg) return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ') c = read();
        boolean neg = (c == '-');
        if (neg) c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
        if (neg) return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1) buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead) fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null) return;
        din.close();
    }
}