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.Scanner;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;

public class D {
	public static void main(String[] args) {
		try {
			BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
			BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));

			int t = Integer.parseInt(reader.readLine());
			for (; t > 0; t--) {
				int n = Integer.parseInt(reader.readLine());
				int[] a = new int[n];
				int[] b = new int[n];

				String[] line = reader.readLine().split(" ");

				for (int i = 0; i < n; i++)
					a[i] = Integer.parseInt(line[i]);

				if (n % 2 == 0) {
					fill(a, b, n);
				} else {
					fill(a, b, n-3);

					b[n-3] = a[n-3] * a[n-1];
					b[n-2] = a[n-2] * a[n-1];

					b[n-1] = -(a[n-3]*a[n-3] + a[n-2]*a[n-2]);
					int g = gcd(gcd(Math.abs(b[n-3]), Math.abs(b[n-2])), Math.abs(b[n-1]));

					for (int i = 1; i <= 3; i++)
						b[n-i] /= g;
				}

				for (int i = 0; i < n; i++) {
					String s = String.valueOf(b[i]);
					writer.write(s, 0, s.length());
					writer.write(' ');
					writer.flush();
				}
			}

			writer.close();
			reader.close();
		} catch (Exception e) { }
	}

	private static int gcd(int a, int b) {
		if (b == 0)	return a;
		return gcd(b, a%b);
	}

	private static void fill(int[] a, int[] b, int lim) {
		for (int i = 0; i < lim; i+=2) {
			int l = a[i]; int r = a[i+1];
			b[i] = -r; b[i+1] = l;

			int g = gcd(Math.abs(b[i]), Math.abs(b[i+1]));
			b[i] /= g; b[i+1] /= g;
		}
	}

	private static void printArr(int[] a) {
		for (Integer i : a)
			System.out.printf("%s ", i);
		System.out.println("");
	}
}