Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn't like the number 0, he threw away all numbers equal to 0 from the array. As a result, he got an array a of length n.

Pupsen, on the contrary, likes the number 0 and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array b of length n such that ∑_{i=1}^{n}a_i ⋅ b_i=0. Since Vupsen doesn't like number 0, the array b must not contain numbers equal to 0. Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed 10^9. Please help Vupsen to find any such array b!

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The next 2 ⋅ t lines contain the description of test cases. The description of each test case consists of two lines.

The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5) — the length of the array.

The second line contains n integers a_1, a_2, …, a_n (-10^4 ≤ a_i ≤ 10^4, a_i ≠ 0) — the elements of the array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print n integers b_1, b_2, …, b_n — elements of the array b (|b_1|+|b_2|+… +|b_n| ≤ 10^9, b_i ≠ 0, ∑_{i=1}^{n}a_i ⋅ b_i=0).

It can be shown that the answer always exists.

Example

Input


3
2
5 5
5
5 -2 10 -9 4
7
1 2 3 4 5 6 7


Output


1 -1
-1 5 1 -1 -1
-10 2 2 -3 5 -1 -1

Note

In the first test case, 5 ⋅ 1 + 5 ⋅ (-1)=5-5=0. You could also print 3 -3, for example, since 5 ⋅ 3 + 5 ⋅ (-3)=15-15=0

In the second test case, 5 ⋅ (-1) + (-2) ⋅ 5 + 10 ⋅ 1 + (-9) ⋅ (-1) + 4 ⋅ (-1)=-5-10+10+9-4=0.
import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.List;
 import java.util.*;
  public class realfast implements Runnable 
  {
    private static final int INF = (int) 1e9;
    long in= 1000000007;
    long fac[]= new long[1000001];
    long inv[]=new long[1000001];
    public  void solve() throws IOException 
    {

        //int t = readInt();

        int t = readInt();
        for(int f =0;f<t;f++)
        {
          int n = readInt();
          int arr[]=new int[n];
          ArrayList<edge> e = new ArrayList<edge>();
          for(int i =0;i<n;i++)
          {
            arr[i]= readInt();
            e.add(new edge(i,arr[i]));
          }
          Collections.sort(e);
          int b[]=new int[n];

          if(n%2==0)
          {
            for(int i =0;i<n;i=i+2)
            {
                 if((arr[i]*arr[i+1])<0)
                 {
                      b[i]= Math.abs(arr[i+1]);
                      b[i+1]= Math.abs(arr[i]);
                 }
                 else
                 {
                    b[i]= - arr[i+1];
                      b[i+1]= arr[i];
                 }
            }

          }
          else
          {
              for(int i =n-1;i>=2;i=i-2)
              {
                  if(i==2)
                  {
                    set3(arr,e.get(2).u,e.get(1).u,e.get(0).u,b);
                  }
                  else
                  {
                    set(arr,e.get(i).u,e.get(i-1).u,b); 
                  }
              }
          }

          for(int i =0;i<n;i++)
            out.print(b[i]+" ");

          out.println();


        }

       
        

    }
    public void set(int arr[] , int i , int j , int brr[])
    {
        if(Math.abs(arr[i])==Math.abs(arr[j]))
        {
            if(arr[i]*arr[j]<0)
            {
                brr[i]=1;
                brr[j]=1;
            }
            else
            {
                brr[i]=-1;
                brr[j]=1;
            }
        }
        else
        {
            if(arr[i]*arr[j]<0)
            {
                brr[i]=Math.abs(arr[j]);
                brr[j]=Math.abs(arr[i]);
            }
            else
            {
                brr[i]=-Math.abs(arr[j]);
                brr[j]=Math.abs(arr[i]);  
            }
        }

    }
    public void set3(int arr[], int i , int j , int k, int brr[])
    {
        if((arr[i]+arr[j])==0)
        {
            if((arr[i]+arr[k])!=0)
            {
                 int temp=j;
                 j=k;
                 k=temp;
            }
            else
            {
                 int temp=i;
                 i=k;
                 k=temp;

            }

        }

        if((arr[i]+arr[j])*arr[k]<0)
        {
            brr[k]=Math.abs(arr[i]+arr[j]);
            brr[i]= Math.abs(arr[k]);
            brr[j]=Math.abs(arr[k]);
        }
        else
        {
             brr[k]=-Math.abs(arr[i]+arr[j]);
            brr[i]= Math.abs(arr[k]);
            brr[j]=Math.abs(arr[k]);

        }



    }
    
    

    
    public int value (int seg[], int left , int right ,int index, int l, int r)
    {
            
            if(left>right)
            {
              return -100000000;
            }
            if(right<l||left>r)
                return -100000000;
            if(left>=l&&right<=r)
                return seg[index];
            int mid = left+(right-left)/2;
            int val = value(seg,left,mid,2*index+1,l,r);
            int val2 = value(seg,mid+1,right,2*index+2,l,r);
            return Math.max(val,val2);

    }
   
    public int gcd(int a , int b )
    {
      if(a<b)
      {
        int t =a;
        a=b;
        b=t;
      }
      if(a%b==0)
        return b ;
      return gcd(b,a%b);
    }
    public long pow(long n , long p,long m)
    {
         if(p==0)
            return 1;
        long val = pow(n,p/2,m);;
        val= (val*val)%m;
        if(p%2==0)
            return val;
        else
            return (val*n)%m;
    }
    
    
    ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
    public static void main(String[] args) {
        new Thread(null, new realfast(), "", 128 * (1L << 20)).start();
    }
 
    private static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
    private BufferedReader reader;
    private StringTokenizer tokenizer;
    private PrintWriter out;
 
    @Override
    public void run() {
        try {
            if (ONLINE_JUDGE || !new File("input.txt").exists()) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                reader = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            solve();
        } catch (IOException e) {
            throw new RuntimeException(e);
        } finally {
            try {
                reader.close();
            } catch (IOException e) {
                // nothing
            }
            out.close();
        }
    }
 
    private String readString() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
 
    @SuppressWarnings("unused")
    private int readInt() throws IOException {
        return Integer.parseInt(readString());
    }
 
    @SuppressWarnings("unused")
    private long readLong() throws IOException {
        return Long.parseLong(readString());
    }
 
    @SuppressWarnings("unused")
    private double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }
}
class edge implements Comparable<edge>{
    int u ;
    int v;
    
    edge(int u, int v)
    {
       this.u=u;
       this.v=v;
    }
    public int compareTo(edge e)
    {
        return Math.abs(this.v)-Math.abs(e.v);
    }
}