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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;

import java.util.*;

public class Main
{

  

    public static void main(String[] args)
    {
        FastScanner input = new FastScanner();
       StringBuilder result = new StringBuilder();
        int tc = input.nextInt();
        while (tc-- > 0) {
          int n = input.nextInt();
      int a[] = new int[n];
      int b[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = input.nextInt();
            
        }
        if(n%2==0)
        {
            for (int i = 0; i <n; i+=2) {
                b[i] = a[i+1];
                b[i+1] = -a[i];
            }
        }
        else
        {
            
            for (int i = 0; i <n-3; i+=2) {
                b[i] = a[i+1];
                b[i+1] = -a[i];
            }
            int last1 = a[n-3];
            int last2 = a[n-2];
            int last3 = a[n-1];
            if(last1+last2!=0)
            {
                b[n-3] = -last3;
                b[n-2] = -last3;
                b[n-1] = (last1+last2);
            }
            else if(last1+last3!=0)
            {
                b[n-3] = -last2;
                b[n-2] = (last1+last3);
                b[n-1] = -last2;
            }
            else if(last2+last3!=0)
            {
                b[n-3] =(last2+last3);
                b[n-2] = -last1;
                b[n-1] = -last1;
            }
        }
        for (int i : b) {
            result.append(i+" ");
        }
        result.append("\n");   
        }
        System.out.println(result);
        
      
    }

    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) {
                }
            }
            return st.nextToken();
        }

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

        long nextLong()
        {

            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine() throws IOException
        {
            return br.readLine();
        }
    }

}
