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 
import java.util.*;
import java.io.*;
import java.util.Scanner;
import java.math.*;
import java.lang.StringBuilder;

public class contest
{
   public static void main(String[] args)
   {
      Scanner scan = new Scanner(System.in);
      
      int n = scan.nextInt();
      int array[] = new int[n];
      int odd = 0;
      int min = 10;
      int minPlace = 0;
      for (int i = 0; i < n; i++)
      {
         array[i] = scan.nextInt();
         if (array[i] > -1)
         {
            array[i] = array[i] * -1 - 1;
         }
         if (array[i] < 0)
         {
            odd = 1 - odd;
         }
         if (array[i] < min)
         {
            min = array[i];
            minPlace = i;
         }
      }
      if (odd == 1)
      {
         if (min < -1 || (/*n == 1 && */min == -1))
         {
            array[minPlace] = array[minPlace] * -1 - 1;
         }
      }
      for (int i = 0; i < n; i++)
      {
         System.out.print(array[i] + " ");
      }
   }
   
   public static boolean isPandigital(int num)
   {
      return true;
   }
}
   
   /*private static int N;
   private static int M;
   
   public static void main(String[] args)
   {
      Scanner scan = new Scanner(System.in);
      N = scan.nextInt();
      M = scan.nextInt();
      
      LineWrapper lineWrapper = new LineWrapper();
      Line line = new Line(scan.nextInt(), scan.nextInt());
      
      lineWrapper.insert(new Line(line));
      for (int i = 1; i < M; i++)
      {
         lineWrapper.insert(new Line(scan.nextInt(), scan.nextInt()));
      }
      lineWrapper.sort();
      
      String comp = lineWrapper.toString();
      
      ArrayList<Integer> possible = new ArrayList<Integer>();
      
      int adder = 1 + N % 2;
      possible.add(0);
      possible.add(1);
      if (N % 2 == 0)
      {
         possible.add(2);
      }
      for (int i = 3; i < N / 2 + 1; i += adder)
      {
         if (N % i == 0)
         {
            possible.add(i);
         }
      }
      
      int i = 0;
      int j;
      int count = 0;
      
      do
      {
         j = 0;
         do
         {
            if (count > possible.size() - 2)
            {
               System.out.print("No");
               System.exit(0);
            }
            line.rotate(possible.get(count + 1) - possible.get(count) - 1);
            j += possible.get(count + 1) - possible.get(count);
            count++;
         } while (!lineWrapper.contains(line));
         
         lineWrapper.rotate(j - 1);
         line.rotate(j - 1);
         i += j;
      } while (!comp.equals(lineWrapper.toString()));
      
      int incr = i;
      i += incr;
      
      if (i > N)
      {
         System.out.print("No");
         System.exit(0);
      }
      for (; i < incr * 3 && i < N / 2 + 1; i += incr)
      {
         lineWrapper.rotate(incr - 1);
         
         if (!comp.equals(lineWrapper.toString()))
         {
            System.out.print("No");
            System.exit(0);
         }
      }
      System.out.print("Yes");
   }
   public static class LineWrapper
   {
      public ArrayList<Line> list;
      
      public LineWrapper()
      {
         list = new ArrayList<Line>();
      }
      
      public void insert(Line line)
      {
         list.add(line);
      }
      
      public void sort()
      {
         Collections.sort(list);
      }
      
      public void rotate(int incr)
      {
         for (Line line: list)
         {
            line.rotate(incr);
         }
         Collections.sort(list);
      }
      
      public boolean contains(Line line)
      {
         int left = 0;
         int right = M - 1;
         int mid = right / 2;
         int temp;
         while (right - left > 1)
         {
            temp = line.compareTo(list.get(mid));
            if (temp < 0)
            {
               right = mid;
            }
            else if (temp > 0)
            {
               left = mid;
            }
            else
            {
               return true;
            }
            mid = (left + right) / 2;
         }
         if (line.compareTo(list.get(right)) == 0 ||
             line.compareTo(list.get(left)) == 0)
         {
            return true;
         }
         return false;
      }
      
      public String toString()
      {
         StringBuilder s = new StringBuilder("");
         for (Line line: list)
         {
            s.append(line.toString());
         }
         return s.toString();
      }
   }
   public static class Line implements Comparable<Line>
   {
      private int a;
      private int b;
      
      public Line(int ain, int bin)
      {
         a = (ain < bin) ? ain : bin;
         b = (ain < bin) ? bin : ain;
      }
      
      public Line(Line line)
      {
         a = line.getA();
         b = line.getB();
      }
      
      public int getA()
      {
         return a;
      }
      
      public int getB()
      {
         return b;
      }
      
      public void rotate(int incr)
      {
         a = ((a + incr) % N) + 1;
         b = ((b + incr) % N) + 1;
         if (a > b)
         {
            int temp = a;
            a = b;
            b = temp;
         }
      }
      
      public String toString()
      {
         return "" + a + b;
      }
      
      @Override
      public int compareTo(Line line)
      {
         if (a < line.getA())
         {
            return -1;
         }
         if (a > line.getA())
         {
            return 1;
         }
         if (b < line.getB())
         {
            return -1;
         }
         if (b > line.getB())
         {
            return 1;
         }
         return 0;
      }
   }
}
      
/*   
      int A = scan.nextInt();
      int B = scan.nextInt();
      int As[];
      int Bs[];
      //0 = n^2 + n - 2(A + B)
      int N = (int) (-1.0 / 2 + 2 * Math.sqrt(1.0 / 16 + (A + B) / 2.0));
      if (B == 0)
      {
         int i = 0;
         while (A > 0 && N > i)
         {
            A -= (N - i);
            i++;
         }
         As = new int[i];
         for (int j = 0; j < i; j++)
         {
            As[j] = N - j;
         }
         System.out.println(i);
         for (int j = 0; j < i; j++)
         {
            System.out.print(As[j] + " ");
         }
         System.out.println("\n0");
      }
      else if (A == 0)
      {
         int i = 0;
         while (B > 0 && N > i)
         {
            B -= (N - i);
            i++;
         }
         Bs = new int[i];
         for (int j = 0; j < i; j++)
         {
            Bs[j] = N - j;
         }
         System.out.println("0\n");
         System.out.println(i);
         for (int j = 0; j < i; j++)
         {
            System.out.print(Bs[j] + " ");
         }
      }
      else if (A <= B)
      {
         int i = 0;
         while (A > N - i)
         {
            A -= (N - i);
            i++;
         }
         As = new int[i + 1];
         for (int j = 0; j < i; j++)
         {
            As[j] = N - j;
         }
         As[i] = A;
         Bs = new int[N - i - 1];
         int k = 0;
         for (int j = (i == 0) ? N : (As[i - 1] - 1); j > 0 && (k < N - i - 1); j--)
         {
            if (j != As[i])
            {
               Bs[k] = j;
               k++;
            }
         }
         System.out.println(i + 1);
         for (int j = 0; j < i + 1; j++)
         {
            System.out.print(As[j] + " ");
         }
         System.out.println("\n" + (N - i - 1));
         for (int j = 0; j < N - i - 1; j++)
         {
            System.out.print(Bs[j] + " ");
         }
      }
      else
      {
         int i = 0;
         while (B > N - i)
         {
            B -= (N - i);
            i++;
         }
         Bs = new int[i + 1];
         for (int j = 0; j < i; j++)
         {
            Bs[j] = N - j;
         }
         Bs[i] = B;
         As = new int[N - i - 1];
         int k = 0;
         for (int j = (i == 0) ? N : (Bs[i - 1] - 1); j > 0 && (k < N - i - 1); j--)
         {
            if (j != Bs[i])
            {
               As[k] = j;
               k++;
            }
         }
         System.out.println(N - i - 1);
         for (int j = 0; j < N - i - 1; j++)
         {
            System.out.print(As[j] + " ");
         }
         System.out.println("\n" + (i + 1));
         for (int j = 0; j < i + 1; j++)
         {
            System.out.print(Bs[j] + " ");
         }
      }
   }
}
      
      /*int N = scan.nextInt();
      int A[] = new int[N - 1];
      int B[] = new int[N - 1];
      int T[] = new int[N];
      for (int i = 0; i < N - 1; i++)
      {
         A[i] = scan.nextInt();
      }
      for (int i = 0; i < N - 1; i++)
      {
         B[i] = scan.nextInt();
      }
      for (int i = 0; i < N - 1; i++)
      {
         while ((T[i] | T[i + 1]) != A[i] ||
                (T[i] & T[i + 1]) != B[i])
         {
            if (T[i + 1] < 3)
            {
               T[i + 1]++;
            }
            else if (T[i] >= 3)
            {
               if (i != 0)
               {
                  T[i - 1]++;
                  T[i] = 0;
                  T[i + 1] = 0;
                  i -= 2;
                  break;
               }
               System.out.print("NO");
               System.exit(0);
            }
            else
            {
               T[i]++;
               T[i + 1] = 0;
               if (i != 0)
               {
                  i -= 2;
                  break;
               }
            }
         }
      }
      System.out.println("YES");
      for (int i = 0; i < N - 1; i++)
      {
         System.out.print(T[i] + " ");
      }
      System.out.print(T[N - 1]);
   }
}*/