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.*;
import java.math.*;

public class Coder {

  static StringBuffer str=new StringBuffer();
  static int n;
  static long a[];

  static void solve(){
    long b[]=new long[n];
    int idx=2;
    if(n%2!=0){
      if(a[0]+a[1] != 0){
        b[0]=-a[2];
        b[1]=-a[2];
        b[2]=a[0]+a[1];
      }else if(a[1]+a[2] != 0){
        b[0]=-a[0];
        b[1]=-a[0];
        b[2]=a[1]+a[2];
      }else{
        b[0]=-a[1];
        b[1]=-a[1];
        b[2]=a[0]+a[2];
      }
      idx++;
    }else{
      b[0]=-a[1];
      b[1]=a[0];
    }
    for(int i=idx;i<n;i+=2){
      b[i]=-a[i+1];
      b[i+1]=a[i];
    }
    for(int i=0;i<n;i++) str.append(b[i]).append(" ");
    str.append("\n");
  }

  public static void main(String[] args) throws java.lang.Exception {
    BufferedReader bf;
    PrintWriter pw;
    boolean lenv=false;
    if(lenv){
      bf = new BufferedReader(
                          new FileReader("input.txt"));
      pw=new PrintWriter(new
            BufferedWriter(new FileWriter("output.txt")));
    }else{
      bf = new BufferedReader(new InputStreamReader(System.in));
      pw = new PrintWriter(new OutputStreamWriter(System.out));
    }
    int q = Integer.parseInt(bf.readLine().trim());
    while (q-- > 0) {
      n=Integer.parseInt(bf.readLine().trim());
      String s[]=bf.readLine().trim().split("\\s+");
      a=new long[n];
      for(int i=0;i<n;i++) a[i]=Long.parseLong(s[i]);
      solve();
    }
    pw.print(str);
    pw.flush();
    // System.out.print(str);
  }
}