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.util.*;
import java.io.*;

////***************************************************************************
 /* public class E_Gardener_and_Tree implements Runnable{

       public static void main(String[] args) throws Exception {
        new Thread(null, new E_Gardener_and_Tree(), "E_Gardener_and_Tree", 1<<28).start();
       }
    public void run(){
         WRITE YOUR CODE HERE!!!!
         JUST WRITE EVERYTHING HERE WHICH YOU WRITE IN MAIN!!!
       }

  }
*/
/////**************************************************************************


public class D_Vupsen_Pupsen_and_0{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
       // PrintWriter out=new PrintWriter(System.out);
        //end of program
        //out.println(answer);
        //out.close();
        StringBuilder res = new StringBuilder();
        int t=s.nextInt();
        int p=0;
        while(p<t){
        int n=s.nextInt();
        long array[]= new long[n];
        for(int i=0;i<n;i++){
            array[i]=s.nextLong();

        }
        long ans[]= new long[n];
        if(n%2==0){
           for(int i=0;i<n;i++){
               if(i%2==0){
                   ans[i]=array[i+1];
               }
               else{
                   ans[i]=(array[i-1]-(2*array[i-1]));
               }
           }
        }
        else{
            int lim=n-3;
            for(int i=0;i<lim;i++){
                if(i%2==0){
                    ans[i]=array[i+1];
                }
                else{
                    ans[i]=(array[i-1]-(2*array[i-1]));
                }
            }
          int a=n-3;
          int b=n-2;
          int c=n-1;
          if(array[a]+array[b]!=0){
            ans[a]=array[c];
            ans[b]=array[c];
            long yo=array[a]+array[b];
            ans[c]=yo-(2*yo);
          }
          else if(array[b]+array[c]!=0){
               ans[b]=array[a];
               ans[c]=array[a];
               long yo=array[b]+array[c];
               ans[a]=yo-(2*yo);
          }
          else{
             ans[a]=array[b];
             ans[c]=array[b];
             long yo=array[a]+array[c];
             ans[b]=yo-(2*yo);
          }
        }
        for(int i=0;i<n;i++){
            res.append(ans[i]+" ");
        }
        res.append("\n");
       p++;
    }
    System.out.println(res);
    

    }
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}




}