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.*;
import java.util.*;

public class Main {
	static MyScanner sc = new MyScanner();
	static Output out=new Output();
	public static void main(String[] args) {
		int t=sc.nextInt();
		for(int i=0;i<t;i++) {
			solve();
		}
		out.flush();
	}
	
	public static void solve() {
	    int n=sc.nextInt();
	    int a[]=sc.nextIntArr(n);
	    int sum=0;
	    for(int i=0;i<n;i++){
	        sum+=a[i];
	    }
	    int in=-1;
	    for(int i=0;i<n;i++){
	        if(sum-a[i]!=0){
	            in=i;
	            break;
	        }
	    }
	    
	    for(int i=0;i<n;i++){
	        if(i!=in)
	            out.print(-a[in]+" ");
	        else
	            out.print(sum-a[in]+" ");
	    }
	    out.println();
	}
}
																																		





















class MyScanner {

	BufferedReader br;
	StringTokenizer st;

	public MyScanner() {
		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;
	}

	public int[] nextIntArr(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArr(int n) {
		double a[] = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public String[] nextArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public String[] nextLineArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLine();
		return a;
	}
}
class Output{
BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
	public void print() {}
	public void println() {
		try {
			out.write("\n");
		}
		catch(Exception e) {}
	}
	public void print(Object s) {
		try {
			out.write(s+"");
		}
		catch(Exception e) {}
	}
	public void println(Object s) {
		try {
			out.write(s+"\n");
		}
		catch(Exception e) {}
	}
	public void flush() {
		try {
			out.flush();
		}
		catch(Exception e){}
	}
}