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 D {
	
//	1
//	10
//	2 5 -1 -7 1 9 -10 18 3 26
	
	public static void main(String[] args)throws IOException {

		FastScanner scan = new FastScanner();
		PrintWriter output = new PrintWriter(System.out);
		int t = scan.nextInt();
		for(int tt = 0;tt<t;tt++) {
			int n = scan.nextInt();
			int arr[] = scan.readArray(n);
			int ans[] = new int[n];
			for(int i = 0;i<n-1;i+=2) {
				ans[i] = arr[i+1];
				ans[i+1] = -arr[i];
			}
			if(n%2==1) {
				int lcm = Math.abs(arr[0]) * Math.abs(arr[n-1]) / gcd(Math.abs(arr[0]), Math.abs(arr[n-1]));
				int add1 = lcm/arr[0];
				int add2 = lcm/arr[n-1];
				if(ans[0]==add1) {
					ans[0]+=add1;
					ans[n-1]-=add2;
				}
				ans[0]-=add1;
				ans[n-1]+=add2;

			}
			for(int i : ans) output.print(i+" ");
//						int sum = 0;
//						for(int i = 0;i<n;i++) {
//							sum+= arr[i]*ans[i];
//						}
			output.println();
//						output.println(sum);
		}
		output.flush();

	}

	public static int[] sort(int arr[]) {

		List<Integer> list = new ArrayList<>();
		for(int i:arr)
			list.add(i);
		Collections.sort(list);
		for(int i = 0;i<list.size();i++) {
			arr[i] = list.get(i);
		}
		return arr;

	}

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

	static boolean isPrime(int n) {
		if (n <= 1) return false;
		else if (n == 2) return true;
		else if (n % 2 == 0) return false;
		for (int i = 3; i <= Math.sqrt(n); i += 2) if (n % i == 0) return false;
		return true;
	}

	public static void printArray(int arr[]) {
		for(int i:arr) System.out.print(i+" ");
		System.out.println();
	}

	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}

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

}
