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 yo {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		for (int xx = 0; xx < t; xx++) {
			int n = sc.nextInt();
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = sc.nextInt();
			}
			if (n % 2 == 0) {
				for (int i = 0; i < n; i = i + 2) {
					pw.append(-arr[i + 1] + " " + arr[i] + " ");
				}
			} else {
				int a = 0;
				int b = 1;
				int c = 2;
				if (arr[a] >= 0 && arr[b] >= 0 && arr[c] >= 0) {
					pw.append(-(arr[b] + arr[c]) + " " + arr[a] + " " + arr[a]+" ");
				} else if (arr[a] < 0 && arr[b] < 0 && arr[c] < 0) {
					pw.append(Math.abs(arr[b] + arr[c]) + " " + arr[a] + " " + arr[a]+" ");
				} else if ((arr[a] >= 0 && arr[b] < 0 && arr[c] < 0) || (arr[a] < 0 && arr[b] >= 0 && arr[c] < 0) || (arr[a] < 0 && arr[b] < 0 && arr[c] >= 0)) {
					if (arr[a] >= 0)
						pw.append((arr[b] + arr[c]) + " " + -arr[a] + " " + -arr[a]);
					else if (arr[b] >= 0)
						pw.append(-arr[b] + " " + (arr[a] + arr[c]) + " " + -arr[b]);
					else
						pw.append(-arr[c] + " " + -arr[c] + " " + (arr[a] + arr[b]));
					pw.append(" ");
				} else {
					if (arr[a] < 0)
						pw.append(-(arr[b] + arr[c]) + " " + arr[a] + " " + arr[a]);
					else if (arr[b] < 0)
						pw.append(arr[b] + " " + -(arr[a] + arr[c]) + " " + arr[b]);
					else
						pw.append(arr[c] + " " + arr[c] + " " + -(arr[a] + arr[b]));
					pw.append(" ");
				}
				for (int i = c + 1; i < n; i = i + 2) {
					pw.append(-arr[i + 1] + " " + arr[i] + " ");
				}
			}
			pw.append("\n");
		}
		pw.flush();
	}
}