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 active;


import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.util.stream.Collectors;

public class Array {

    public static void main(String[] args) {
        final int n = sc.nextInt();
        List<Integer> array = new ArrayList<>();
        List<Integer> firstSet, secondSet = new ArrayList<>(),
                thirdSet = new ArrayList<>();
        int zeroCount = 0, negativeCount = 0;
        int no;
        for (int i = 0; i < n; i++) {
            no = sc.nextInt();
            if (no == 0) {
                zeroCount++;
                thirdSet.add(no);
            } else if (no < 0) {
                negativeCount++;
            } else {
                secondSet.add(no);
            }
            array.add(no);
        }
        
        List<Integer> onlyNegativeList = new ArrayList(array.stream().filter(e -> e < 0).collect(Collectors.toList()));
        if (secondSet.isEmpty()) {
            secondSet.add(onlyNegativeList.get(0));
            secondSet.add(onlyNegativeList.get(1));
            onlyNegativeList.remove(0);
            onlyNegativeList.remove(0);
        }
        
        if (isEven(negativeCount)) {
            thirdSet.add(onlyNegativeList.get(0));
            onlyNegativeList.remove(0);
        }
        
        firstSet = onlyNegativeList;
        
        out.println(firstSet.size() + " " + join(firstSet, " "));
        out.println(secondSet.size() + " " + join(secondSet, " "));
        out.println(thirdSet.size() + " " + join(thirdSet, " "));
        
        out.close();
    }

    
    /** Helpers **/
    
    // Math
    private static boolean isEven(int a) {
        return a % 2 == 0;
    }
    
    private static long gcd(long a, long b) {
        if (a == 0) {
            return b;
        }
        
        return gcd(b % a, a);
    }
    
    // String
    
    private static String join(List<Integer> list, String separator) {
        StringBuilder builder = new StringBuilder();
        
        list.forEach(e -> builder.append(e).append(separator));
        
        return builder.toString().trim();
    }
    
    // IO
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
    static final FastScanner sc = new FastScanner();

    public static class FastScanner {

        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}