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.*;
import java.io.*;

public class D_1582 {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = sc.nextInt();
		while(t-->0) {
			int n = sc.nextInt();
			int[] a = sc.nextIntArray(n);
			
			ArrayList<Integer>[] list = new ArrayList[(int)2e4+1];
			for(int i = 0; i < list.length; i++)
				list[i] = new ArrayList<>();
			
			for(int i = 0; i < n; i++)
				list[a[i] + (int)1e4].add(i);
			
			ArrayList<Integer> ones = new ArrayList<>();
			for(int i = 0; i < list.length; i++)
				if(list[i].size() == 1) {
					for(int j : list[i])
						ones.add(j);
					list[i] = new ArrayList<>();
				}
			
			if(ones.size() == 1) {
				for(int i = 0; i < list.length; i++) {
					if(list[i].size() == 2) {
						for(int j : list[i])
							ones.add(j);
						list[i] = new ArrayList<>();
						break;
					} else if(list[i].size() > 2) {
						int x = list[i].get(list[i].size() - 1);
						ones.add(x);
						list[i].remove(list[i].size() - 1);
						break;
					}
				}
			}
			
			int[] b = new int[n];
			int index = 0;
			if(ones.size() % 2 == 1) {
				int x = ones.get(0), y = ones.get(1), z = ones.get(2);
				b[x] = 2 * a[y] * a[z];
				b[y] = -1 * a[x] * a[z];
				b[z] = -1 * a[x] * a[y];
				index = 3;
			}
			for(int i = index; i < ones.size(); i += 2) {
				int x = ones.get(i), y = ones.get(i + 1);
				b[x] = a[y];
				b[y] = -1 * a[x];
			}
			for(int i = 0; i < list.length; i++) {
				if(list[i].size() > 0) {
					for(int j = 0; j < list[i].size() - 1; j++)
						b[list[i].get(j)] = 1;
					b[list[i].get(list[i].size() - 1)] = -1 * (list[i].size() - 1);
				}
			}
			
			for(int i = 0; i < n; i++)
				pw.print(b[i] + (i == n - 1 ? "\n" : " "));
		}
		
		pw.flush();
	}

	public static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] array = new Integer[n];
			for (int i = 0; i < n; i++)
				array[i] = new Integer(nextInt());
			return array;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

		public double[] nextDoubleArray(int n) throws IOException {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		public static int[] shuffle(int[] a) {
			int n = a.length;
			Random rand = new Random();
			for (int i = 0; i < n; i++) {
				int tmpIdx = rand.nextInt(n);
				int tmp = a[i];
				a[i] = a[tmpIdx];
				a[tmpIdx] = tmp;
			}
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}
