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.
/*==========================================================================
*   	AUTHOR:    RonWonWon
*   	CREATED:   24.10.2021 17:30:32        
/*==========================================================================*/
import java.io.*;
import java.util.*;

public class D {
	
	public static void main(String[] args) throws IOException {
		/*
    in.ini();
    PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    */
    long startTime = System.nanoTime();
    int t = in.nextInt(), T = 1;  
    while(t-->0) { 
      int n = in.nextInt();
      int a[] = in.readArray(n);
      Pair b[] = new Pair[n];
      for(int i=0;i<n;i++) b[i] = new Pair(i,Math.abs(a[i])); 
      Arrays.sort(b);
      int ans[] = new int[n];
      int i = n-1;
      while(i>-1){
      	Pair v1 = b[i];
      	if(i-1==1){
      		Pair v2 = b[i-1], v3 = b[i-2];
      		int id1 = v1.x, id2 = v2.x, id3 = v3.x;
      		if(a[id1]<0) ans[id1] = (-(v2.y+v3.y));
      		else ans[id1] = ((v2.y+v3.y));
      		if(a[id2]>0) ans[id2] = (-v1.y);
      		else ans[id2] = (v1.y);
      		if(a[id3]>0) ans[id3] = (-v1.y);
      		else ans[id3] = (v1.y);
      		break;
      	}
      	else{
      		Pair v2 = b[i-1];
      		int id1 = v1.x, id2 = v2.x;
      		if(a[id1]<0) ans[id1] = (-v2.y);
      		else ans[id1] = (v2.y);
      		if(a[id2]>0) ans[id2] = (-v1.y);
      		else ans[id2] = (v1.y);
      		i-=2;
      	}
      }
      for(int ii : ans) out.print(ii+" ");
      out.println();
   		//out.println("Case #"+T+": "+ans); T++;
    }
    /*
    startTime = System.nanoTime() - startTime;
    System.err.println("Time: "+(startTime/1000000));
    */
    out.flush();
	}
	
	static class Pair implements Comparable<Pair> {
		int x, y;
		Pair(int a, int b){ x = a; y = b; }		
		@Override
		public int compareTo(Pair o) {
			return y - o.y;
		}
	}
	
	static FastScanner in = new FastScanner();
  static PrintWriter out = new PrintWriter(System.out);
	static int oo = Integer.MAX_VALUE;
	static long ooo = Long.MAX_VALUE;
	
	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		
		void ini() throws FileNotFoundException {
			br = new BufferedReader(new FileReader("input.txt"));
		}
		
		String next() {
			while(!st.hasMoreTokens())
				try { st = new StringTokenizer(br.readLine()); }
				catch(IOException e) {}
			return st.nextToken();
		}
		
		String nextLine(){
			try{ return br.readLine(); } 
			catch(IOException e) { } return "";
		}
		
		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());
		}
		
		long[] readArrayL(int n) {
			long a[] = new long[n];
			for(int i=0;i<n;i++) a[i] = nextLong();
			return a;
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
		
		double[] readArrayD(int n) {
			double a[] = new double[n];
			for(int i=0;i<n;i++) a[i] = nextDouble();
			return a;
		}
	}

	static final Random random = new Random();

	static void ruffleSort(int[] a){
		int n = a.length;
		for(int i=0;i<n;i++){
			int j = random.nextInt(n), temp = a[j];
			a[j] = a[i]; a[i] = temp;
		}
		Arrays.sort(a); 	
	}
	
	static void ruffleSortL(long[] a){
		int n = a.length;
		for(int i=0;i<n;i++){
			int j = random.nextInt(n);
			long temp = a[j];
			a[j] = a[i]; a[i] = temp;
		}
		Arrays.sort(a); 	
	}
}
