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.
//#Rohitpratap311
//Keep_Calm_And_Stay_Happy
import java.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=input.nextInt();
        while(T-->0)
        {
            int n=input.nextInt();
            int a[]=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=input.nextInt();
            }
            int b[]=new int[n];
            if(n%2==0)
            {
                for(int i=0;i<n;i+=2)
                {
                    int v1=Math.abs(a[i]),v2=Math.abs(a[i+1]);
                    int l=lcm(v1,v2);
                    int x=l/v1,y=l/v2;
                    if((a[i]>=0 && a[i+1]<0) || (a[i]<0 && a[i+1]>=0))
                    {
                        b[i]=x;
                        b[i+1]=y;
                    }
                    else
                    {
                        b[i]=x;
                        b[i+1]=-y;
                    }
                }
                for(int i=0;i<n;i++)
                {
                    out.print(b[i]+" ");
                }
                out.println();
            }
            else
            {
                for(int i=0;i<n-3;i+=2)
                {
                    int v1=Math.abs(a[i]),v2=Math.abs(a[i+1]);
                    int l=lcm(v1,v2);
                    int x=l/v1,y=l/v2;
                    if((a[i]>=0 && a[i+1]<0) || (a[i]<0 && a[i+1]>=0))
                    {
                        b[i]=x;
                        b[i+1]=y;
                    }
                    else
                    {
                        b[i]=x;
                        b[i+1]=-y;
                    }
                }
                int l1=lcm(Math.abs(a[n-3]),Math.abs(a[n-2]));
                int x=l1/Math.abs(a[n-3]),y=l1/Math.abs(a[n-2]);
                int l2=lcm(Math.abs(a[n-3]),Math.abs(a[n-1]));
                int z=l2/Math.abs(a[n-3]);
                if((a[n-3]>=0 && a[n-2]<0) || (a[n-3]<0 && a[n-2]>=0))
                {

                }
                else
                {
                    y=-y;
                }
                x+=z;
                int sum=a[n-3]*x+a[n-2]*y;
                sum=-sum;
                z=sum/a[n-1];
                b[n-3]=x;
                b[n-2]=y;
                b[n-1]=z;
                for(int i=0;i<n;i++)
                {
                    out.print(b[i]+" ");
                }
                out.println();
            }
        }
        out.close();
    }
    public static int gcd(int a, int b)
    {
        if(a==0)
        {
            return b;
        }
        else
        {
            return gcd(b%a,a);
        }
    }
    public static int lcm(int a, int b)
    {
        return (a/gcd(a,b))*b;
    }
    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;
        }
    }
}