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.*;

public class cf2
{
	static Scanner sc = new Scanner(System.in);

	private static void solve()
	{
		int n = sc.nextInt();
		int a[] = new int[n];
		for(int i=0; i<n; ++i) {
			a[i] = sc.nextInt();
		}

		if(n%2==0) {
			for(int i=0; i<n; ++i) {
				if(i%2==0)System.out.print(a[i+1]+" ");
				else System.out.print(-a[i-1]+" ");
			}
			System.out.println();
			return;
		}
		for(int i=0; i<n-3; ++i) {
				if(i%2==0)System.out.print(a[i+1]+" ");
				else System.out.print(-a[i-1]+" ");
		}

		if(a[n-3]+a[n-2]!=0) System.out.print(-(a[n-1])+" "+(-a[n-1])+ " "+(a[n-3]+a[n-2]));
		else if (a[n-3]+a[n-1]!=0)
			System.out.print(-a[n-2]+" "+(a[n-3]+a[n-1])+" "+(-a[n-2]));
		else System.out.print((a[n-2]+a[n-1])+" "+(-a[n-3])+" "+(-a[n-3]));
			System.out.println();
	}
	public static void main (String args[])
	{
		int t = sc.nextInt();
		while(t-->0)solve();
		sc.close();
	}
}
