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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class A300 {
	public static void main(String[] args)throws Exception{
		int n = IO.nextInt();
		int d[] = IO.nextIntArray(n, " ");
		int negc=0;
		ArrayList<Integer> negative = new ArrayList<>();
		ArrayList<Integer> positive = new ArrayList<>();
		
		for(int i=1;i<=n;++i){	
			if(d[i]<0){
				negc++;
				negative.add(i);
			}else if(d[i]>0){
				positive.add(i);
			}
		}

		IO.print(1+" "+d[negative.get(0)]+"\n");
		
		if(negc%2==1){
			IO.print(positive.size()+negative.size()-1);
			for(int i=1;i<negative.size();++i){
				IO.print(" "+d[negative.get(i)]);
			}
			for(int i=0;i<positive.size();++i){
				IO.print(" "+d[positive.get(i)]);
			}
			IO.println();
			IO.println(1+" 0");
		}else{
			IO.print(negc-2+positive.size());
			for(int i=2;i<negative.size();++i){
				IO.print(" "+d[negative.get(i)]);
			}
			for(int i=0;i<positive.size();++i){
				IO.print(" "+d[positive.get(i)]);
			}
			IO.println();
			IO.println(2+" 0"+" "+d[negative.get(1)]);
			
		}
	}
	
	static class IO{

	    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	
	    public static int[][] next2dInt(int rows, int cols, String seperator) throws Exception {
	        int[][] arr = new int[rows + 1][cols + 1];
	        for (int i = 1; i <= rows; ++i) {
	            arr[i] = nextIntArray(cols, seperator);
	        }
	        return arr;
	    }
	
	    public static int[] nextIntArray(int nInts, String seperator) throws IOException {
	        String ints = br.readLine();
	        String[] sArray = ints.split(seperator);
	        int[] array = new int[nInts + 1];
	        for (int i = 1; i <= nInts; ++i) {
	            array[i] = Integer.parseInt(sArray[i - 1]);
	        }
	        return array;
	    }
	
	    public static long[] nextLongArray(int nLongs, String seperator) throws IOException {
	        String longs = br.readLine();
	        String[] sArray = longs.split(seperator);
	        long[] array = new long[nLongs + 1];
	        for (int i = 1; i <= nLongs; ++i) {
	            array[i] = Long.parseLong(sArray[i - 1]);
	        }
	        return array;
	    }
	
	    public static double[] nextDoubleArray(int nDoubles, String seperator) throws IOException {
	        String doubles = br.readLine();
	        String[] sArray = doubles.split(seperator);
	        double[] array = new double[nDoubles + 1];
	        for (int i = 1; i <= nDoubles; ++i) {
	            array[i] = Double.parseDouble(sArray[i - 1]);
	        }
	        return array;
	    }
	
	    public static char[] nextCharArray(int nChars, String seperator) throws IOException {
	        String chars = br.readLine();
	        String[] sArray = chars.split(seperator);
	        char[] array = new char[nChars + 1];
	        for (int i = 1; i <= nChars; ++i) {
	            array[i] = sArray[i - 1].charAt(0);
	        }
	        return array;
	    }
	
	    public static int nextInt() throws IOException {
	        String in = br.readLine();
	        return Integer.parseInt(in);
	    }
	
	    public static double nextDouble() throws IOException {
	        String in = br.readLine();
	        return Double.parseDouble(in);
	    }
	
	    public static long nextLong() throws IOException {
	        String in = br.readLine();
	        return Long.parseLong(in);
	    }
	
	    public static int nextChar() throws IOException {
	        String in = br.readLine();
	        return in.charAt(0);
	    }
	
	    public static String nextString() throws IOException {
	        return br.readLine();
	    }
	
	    public static void print(Object... o) {
	        for (Object os : o) {
	            System.out.print(os);
	        }
	    }
	
	    public static void println(Object... o) {
	        for (Object os : o) {
	            System.out.print(os);
	        }
	        System.out.print("\n");
	    }
	
	    public static void printlnSeperate(String seperator, Object... o) {
	        StringBuilder sb = new StringBuilder();
	        sb.delete(sb.length() - seperator.length(), sb.length());
	        System.out.println(sb);
	    }
	}
}