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.
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
//    static int mod = 998244353 ;
//    static int N = 200005;
//    static long factorial_num_inv[] = new long[N+1];
//    static long natual_num_inv[] = new long[N+1];
//    static long fact[] = new long[N+1];
//    static void InverseofNumber() 
//{ 
//    natual_num_inv[0] = 1;
//    natual_num_inv[1] = 1; 
//    for (int i = 2; i <= N; i++) 
//        natual_num_inv[i] = natual_num_inv[mod % i] * (mod - mod / i) % mod; 
//} 
//static void InverseofFactorial() 
//{ 
//    factorial_num_inv[0] = factorial_num_inv[1] = 1; 
  
//    for (int i = 2; i <= N; i++) 
//        factorial_num_inv[i] = (natual_num_inv[i] * factorial_num_inv[i - 1]) % mod; 
//} 
//static long nCrModP(long N, long R) 
//{ 
//    long ans = ((fact[(int)N] * factorial_num_inv[(int)R]) % mod * factorial_num_inv[(int)(N - R)]) % mod; 
//    return ans%mod; 
//}
    //static boolean prime[];
    //static void sieveOfEratosthenes(int n)
    //{
    //    prime = new boolean[n+1];
        
    //    for (int i = 0; i <= n; i++)
    //        prime[i] = true;
 
    //    for (int p = 2; p * p <= n; p++)
    //    {
    //        // If prime[p] is not changed, then it is a
    //        // prime
    //        if (prime[p] == true)
    //        {
    //            // Update all multiples of p
    //            for (int i = p * p; i <= n; i += p)
    //                prime[i] = false;
    //        }
    //    }
 
        
    //}
    
	public static void main (String[] args) throws java.lang.Exception
	{
    //    InverseofNumber();
    //    InverseofFactorial();
    //   fact[0] = 1; 
    //   for (long i = 1; i <= 2*100000; i++)
    //   { 
    //       fact[(int)i] = (fact[(int)i - 1] * i) % mod; 
    //   }
    
		FastReader scan = new FastReader();
		PrintWriter pw = new PrintWriter(System.out);
        int t = scan.nextInt();
        while(t-->0){
         int n= scan.nextInt();
         long a[] = new long[n];
         for(int i=0;i<n;i++){
             a[i] = scan.nextLong();
         }
         long b[] = new long[n];
         int i=0;
         if(n%2==1){
           if(a[0]+a[1]!=0){
           b[0] = -1*a[2];
           b[1] = -1*a[2];
           b[2] = a[0]+a[1];}
           else if(a[0]+a[2]!=0){
            b[0] = -1*a[1];
            b[2] = -1*a[1];
            b[1] = a[0]+a[2];
           }
           else{
            b[2] = -1*a[0];
            b[1] = -1*a[0];
            b[0] = a[2]+a[1]; 
           }
           i = 3;
         }
         else{
             b[0] = -a[1];
             b[1] = a[0];
             i=2;
         }
         while(i<n-1){
             b[i] = -a[i+1];
             b[i+1] = a[i];
             i = i+2;
         }
         for(int j=0;j<n;j++){
             pw.print(b[j]+" ");
         }
         pw.println();
         pw.flush();
        }
    
    }
    
//   static long gcd(long a,long b){
//       if(a==0)
//       return b;
//       return gcd(b%a,a);
//   }
//   static long lcm(long a,long b){
//       return (a/gcd(a,b))*b;
//   }
}
//class Pair{
//    Integer x,y;
//    Pair(int x,int y){
//        this.x = x;
//        this.y = y;
//    }
//    public boolean equals(Object obj) {
//        // TODO Auto-generated method stub
//        if(obj instanceof Pair)
//        {
//            Pair temp = (Pair) obj;
//            if(this.x.equals(temp.x) && this.y.equals(temp.y))
//                return true;
//        }
//        return false;
//    }

//    @Override
//    public int hashCode() {
//        // TODO Auto-generated method stub
        
//        return (this.x.hashCode() + this.y.hashCode());        
//    }
//}
//class Compar implements Comparator<Pair>{
//    public int compare(Pair p1,Pair p2){
//        return p1.x-p2.x;
//    }
//}
