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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class D {
    public static void main(String[] args)
    {
        FastScanner sc=new FastScanner();
        int t=sc.nextInt();
        PrintWriter pw=new PrintWriter(System.out);
        while(t-->0) {
            int n=sc.nextInt();
            int[] a=sc.readArray(n);
            long sum=0;
            for(int x:a){
                sum+=x;
            }
            int[] ans=new int[n];
            Arrays.fill(ans,-1);
            if(sum==0){
                for(int i=0;i<n;i++){
                    pw.print(-1+" ");
                }
                pw.println();
                continue;
            } else if(sum>0) {
                int idx=-1;
                int max=Integer.MIN_VALUE;
                for(int i=0;i<n;i++){
                    if(sum%Math.abs(a[i])==0){
                        if(Math.abs(a[i])>max){
                            max=Math.abs(a[i]);
                            idx=i;
                        }
                    }
                }
                if(idx==-1){
                    continue;
                }
                ans[idx]= (int) ((sum-a[idx])/a[idx]);
            } else {
                int idx=-1;
                int max=Integer.MIN_VALUE;
                for(int i=0;i<n;i++){
                    if(Math.abs(sum)%Math.abs(a[i])==0){
                        if(Math.abs(a[i])>max){
                            max=Math.abs(a[i]);
                            idx=i;
                        }
                    }
                }
                if(idx==-1){
                    continue;
                }
                ans[idx]= (int) ((sum-a[idx])/a[idx]);
            }
            for(int x:ans){
                pw.print(x+" ");
            }
            pw.println();
        }
        pw.flush();
    }

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

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
}
