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;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import java.util.StringTokenizer;
public class A{
// author: Tarun Verma
static FastScanner sc = new FastScanner();
static int inf = Integer.MAX_VALUE;
static long mod = 1000000007;

static boolean isPalindrom(char[] arr, int i, int j) {
	boolean ok = true;
	while (i <= j) {
		if (arr[i] != arr[j]) {
			ok = false;
			break;
		}
		i++;
		j--;
	}
	return ok;
}

static int max(int a, int b) {
	return Math.max(a, b);
}

static int min(int a, int b) {
	return Math.min(a, b);
}

static long max(long a, long b) {
	return Math.max(a, b);
}

static long min(long a, long b) {
	return Math.min(a, b);
}

static int abs(int a) {
	return Math.abs(a);
}

static long abs(long a) {
	return Math.abs(a);
}

static void swap(long arr[], int i, int j) {
	long temp = arr[i];
	arr[i] = arr[j];
	arr[j] = temp;
}

static void swap(int arr[], int i, int j) {
	int temp = arr[i];
	arr[i] = arr[j];
	arr[j] = temp;
}

static int maxArr(int arr[]) {
	int maxi = Integer.MIN_VALUE;
	for (int x : arr)
		maxi = max(maxi, x);
	return maxi;
}

static int minArr(int arr[]) {
	int mini = Integer.MAX_VALUE;
	for (int x : arr)
		mini = min(mini, x);
	return mini;
}

static long maxArr(long arr[]) {
	long maxi = Long.MIN_VALUE;
	for (long x : arr)
		maxi = max(maxi, x);
	return maxi;
}

static long minArr(long arr[]) {
	long mini = Long.MAX_VALUE;
	for (long x : arr)
		mini = min(mini, x);
	return mini;
}

static long gcd(int a, int b) {
	if (b == 0)
		return a;
	return gcd(b, a % b);
}

static long gcd(long a, long b) {
	if (b == 0)
		return a;
	return gcd(b, a % b);
}

static void ruffleSort(int[] a) {
	int n = a.length;
	Random r = new Random();
	for (int i = 0; i < a.length; i++) {
		int oi = r.nextInt(n);
		int temp = a[i];
		a[i] = a[oi];
		a[oi] = temp;
	}
	Arrays.sort(a);
}

public static int binarySearch(int a[], int target) {
	int left = 0;
	int right = a.length - 1;
	int mid = (left + right) / 2;
	int i = 0;
	while (left <= right) {
		if (a[mid] <= target) {
			i = mid + 1;
			left = mid + 1;
		} else {
			right = mid - 1;
		}
		mid = (left + right) / 2;
	}
	return i;
}

static class FastScanner {
	BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	StringTokenizer st = new StringTokenizer("");

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

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

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

	int[][] read2dArray(int n, int m) {
		int arr[][] = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				arr[i][j] = nextInt();
			}
		}
		return arr;
	}

	ArrayList<Integer> readArrayList(int n) {
		ArrayList<Integer> arr = new ArrayList<Integer>();
		for (int i = 0; i < n; i++) {
			int a = nextInt();
			arr.add(a);
		}
		return arr;
	}

	long nextLong() {
		return Long.parseLong(next());
	}
}
////////////////////////////////////////////////////////////////////////////////////
////////////////////DO NOT TOUCH BEFORE THIS LINE //////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////

public static void main(String[] args) {
	int t = 1;
//	t = sc.nextInt();
	for (int tt = 0; tt < t; tt++) {
		int n = sc.nextInt();
		int arr[] = sc.readArray(n);
		int cnt = 0;
		for(int x: arr) {
			if(x<0) cnt++;
		}
		ArrayList<Integer> ans = new ArrayList<Integer>();
		ruffleSort(arr);
		int i = 0;
		if((cnt & 1) == 0) {
			System.out.println(1 + " " + arr[0]);
			i++;
			if(cnt - 2 > 0) {
				System.out.print((cnt-2) + " ");
				for(;i<=cnt-2;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
				System.out.print(n - (cnt - 1) + " ");
				for(;i<n;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
			} else {
				System.out.println(1 + " " + arr[n-1]);
				System.out.print((n-2) + " ");
				for(;i<n-1;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
			}
		} else {
			System.out.println(1 + " " + arr[0]);
			i++;
			cnt--;
			if(cnt > 0) {
				System.out.print(cnt + " ");
				for(;i<=cnt;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
				cnt++;
				System.out.print((n - cnt)+" ");
				for(;i<n;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
			} else {
				System.out.println(1 + " " + arr[n-1]);
				System.out.print((n - 2) + " ");
				for(;i<n-1;i++) {
					System.out.print(arr[i] + " ");
				}System.out.println();
			}
		}
		
			
		
	}
}

////////////////////////////////////////////////////////////////////////////////////	
//////////////////THIS IS THE LAST CHANCE!!!!!//////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////

}