Nick had received an awesome array of integers a=[a_1, a_2, ..., a_n] as a gift for his 5 birthday from his mother. He was already going to explore its various properties but after unpacking he was disappointed a lot because the product a_1 ⋅ a_2 ⋅ ... a_n of its elements seemed to him not large enough.

He was ready to throw out the array, but his mother reassured him. She told him, that array would not be spoiled after the following operation: choose any index i (1 ≤ i ≤ n) and do a_i := -a_i - 1.

For example, he can change array [3, -1, -4, 1] to an array [-4, -1, 3, 1] after applying this operation to elements with indices i=1 and i=3. 

Kolya had immediately understood that sometimes it's possible to increase the product of integers of the array a lot. Now he has decided that he wants to get an array with the maximal possible product of integers using only this operation with its elements (possibly zero, one or more times, as many as he wants), it is not forbidden to do this operation several times for the same index. 

Help Kolya and print the array with the maximal possible product of elements a_1 ⋅ a_2 ⋅ ... a_n which can be received using only this operation in some order.

If there are multiple answers, print any of them.

Input

The first line contains integer n (1 ≤ n ≤ 10^{5}) — number of integers in the array.

The second line contains n integers a_1, a_2, …, a_n (-10^{6} ≤ a_i ≤ 10^{6}) — elements of the array

Output

Print n numbers — elements of the array with the maximal possible product of elements which can be received using only this operation in some order from the given array.

If there are multiple answers, print any of them.

Examples

Input


4
2 2 2 2


Output


-3 -3 -3 -3 

Input


1
0


Output


0 

Input


3
-3 -3 2


Output


-3 -3 2 
/*
 * No package must be added here because some Online Judges don't support it
 * please remove, if any.
 * 
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

/*
 * Only classes with 'Main' name are accepted in CodeChef and some other online judges
 */
public class NickAndArray {

	/*
	 * In a Programming contest, you are expected to print the output at the
	 * end, so `output` variable will hold all the processed results till the
	 * end
	 */
	// Program's starting point
	public static void main(String[] args) {

		/*
		 * A Scanner class slows down Input/Output a LOT ,thereby increasing
		 * your code execution time , Hence for best results that is Fast I/O
		 * try to use BufferedReader
		 */
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		/*
		 * Generally Code Chef, Hacker Rank gives X number of test cases so we
		 * process the input for each.
		 */
		final int cases=1;
		try {
			/*
			 * Logic of the program must be separated from the meta code to
			 * increase readability and help debugging easier
			 * Also note that Solver object is created inside for loop to
			 * avoid multiple object creation that drastically increases 
			 * execution time and memory usage
			 */
			Solver solver = new Solver();
			for (int i = 0; i < cases; i++) {	
			    int n=Integer.parseInt(br.readLine());
			    String ar[]=br.readLine().split(" ");
			    int arr[]=new int[n];
			    for(int j=0;j<n;j++)
			    	arr[j]=Integer.parseInt(ar[j]);		
				solver.solve(arr);
			}
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
	}
}
/*
 * Some basic rules while coding in Programming Contests:
 * Try to follow at least 80% of them
	Correctness
		- final declaration for required data types
		- avoid Object creation 
		- Scanner slows down, use InputReader
		- avoid too many static functions	
	Efficiency
		- use library functions as much as possible		
		- assertEquals("RESULT", functionToCall())
	Debugging-ability
		- avoid too many global variables 
		- Separate logic from meta-processing
		- variable/function pneumonics must make sense
 * 
 */
class Solver extends NickAndArray{
	/*
	 * Logic goes here ...
	 * Add to the global variables after processing the input
	 * Maybe reverse a string or parse to an integer or , etc.
	 */
	public void solve(int arr[]) {
		int n=arr.length;
	    long max=1000000;
	    int ind=-1;
		for(int i=0;i<n;i++)
		{
           if(arr[i]>=0)
           	   arr[i]=((-1)*arr[i])-1;
           	if(arr[i]<max & arr[i]!=-1)
           	{
           		max=arr[i];
           		ind=i;
           	}
	    }
	    if(n%2==1)
	    {
	    	if(max==1000000)
	    	{
	    		max=-1;
	    		ind=0;
	    	}
	    	arr[ind]=-arr[ind]-1;
	    }
	    for(int i=0;i<n;i++)
	    	System.out.print(arr[i]+" ");
	}
}