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.util.Arrays;
import java.util.StringTokenizer;

public class VupsenPupsenAnd0 {
	
	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 nextFloat() { return Float.parseFloat(next()); }
 
        double nextDouble() { return Double.parseDouble(next()); }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] nextArray(int n)
        {
        	int[] a = new int[n];
        	for (int i=0; i<n; i++) {
        		a[i] = this.nextInt();
        	}
        	return a;
        }
        
        long[] nextArrayLong(int n)
        {
        	long[] a = new long[n];
        	for (int i=0; i<n; i++) {
        		a[i] = this.nextInt();
        	}
        	return a;
        }
        
    }
	
	static class Pair {
		
		int a, b;

		public Pair(int a, int b) {
			
			this.a = a;
			this.b = b;
			
		}

	}

	public static void solve(int n, int[] a) {
		
		StringBuilder ans = new StringBuilder();
		if ((n&1) == 0) {
			for (int i=0; i<n; i+=2) {
				ans.append(a[i+1] + " " + (-a[i]) + " ");
			}
		}
		else {
			Pair[] b = new Pair[3];
			for (int i=0; i<3; i++) {
				b[i] = new Pair(i, a[i]);
			}
			if (b[0] == b[1] && b[1] == b[2]) {
				ans.append("-1 -1 2 ");
			}
			else {
				Arrays.sort(b, (P1, P2) -> P1.b - P2.b);
				int x = b[1].b;
				int y = b[2].b-b[0].b;
				int z = -b[1].b;
				b[0].b = x;
				b[1].b = y;
				b[2].b = z;
				Arrays.sort(b, (P1, P2) -> P1.a - P2.a);
				ans.append(b[0].b + " " + b[1].b + " " + b[2].b + " ");
			}
			for (int i=3; i<n; i+=2) {
				ans.append(a[i+1] + " " + (-a[i]) + " ");
			}
		}
		System.out.println(ans);
		
	}

	public static void main(String[] args) {
		
		FastReader in = new FastReader();
		int t = in.nextInt();
		while (t-- > 0) {
			int n = in.nextInt();
			int[] a = in.nextArray(n);
			solve(n, a);
		}

	}

}
