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.
/*
                       _oo0oo_
                      o8888888o
                      88" . "88
                      (| -_- |)
                      0\  =  /0
                    ___/`---'\___
                  .' \\|     |// '.
                 / \\|||  :  |||// \
                / _||||| -:- |||||- \
               |   | \\\  -  /// |   |
               | \_|  ''\---/''  |_/ |
               \  .-\__  '-'  ___/-. /
             ___'. .'  /--.--\  `. .'___
          ."" '<  `.___\_<|>_/___.' >' "".
         | | :  `- \`.;`\ _ /`;.`/ - ` : | |
         \  \ `_.   \_ __\ /__ _/   .-` /  /
     =====`-.____`.___ \_____/___.-`___.-'=====
                       `=---='
 
*/

import java.util.*;
import java.math.*;
import java.io.*;
import java.lang.Math.*;

public class KickStart2020 {
	 static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		float nextFloat() {
			return Float.parseFloat(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);

	}

	static long lcm(long a, long b) {
		return a / gcd(a, b) * b;
	}

	public static class Pair implements Comparable<Pair> {
		public long index;
		public int z;
		public int[] value;

		public Pair(long index, int z, int value[]) {
			this.index = index;
			this.z = z;
			this.value = value;
		}

		@Override
		public int compareTo(Pair other) {
			// multiplied to -1 as the author need descending sort order
			if(other.index < this.index) return 1;
			if(other.index > this.index) return -1;
			else return 0;
		}
		@Override
		public String toString() {
			return this.index + " " + this.value;
		}
	}
	static boolean isPrime(long d) {
		if (d == 1)
			return false;
		for (int i = 2; i <= (long) Math.sqrt(d); i++) {
			if (d % i == 0)
				return false;
		}
		return true;
	}
	static void decimalTob(int n, int k, Stack<Integer> ss) {
          int x = n % k;
          int y = n / k;
          ss.push(x);
          if(y > 0) {
        	   decimalTob(y, k, ss);
          }
	}
	static long powermod(long x, long y, long mod) {
		long ans = 1;
		x = x % mod;
		if (x == 0)
			return 0;
		int i = 1;
		while (y > 0) {
			if ((y & 1) != 0)
				ans = (ans * x) % mod;
			y = y >> 1;
			x = (x * x) % mod;
		}
		return ans;
	}
	public static void main(String[] args) throws Exception {
		FastReader sc = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		int t = sc.nextInt();
		outerloop:
			while(t-- > 0) {
               int n = sc.nextInt();
               long arr[] = new long[n];
              for(int i = 0; i < n; i++) {
            	  arr[i] = sc.nextInt();
              }
              if(n % 2 == 1) {
            	  for(int i = 0; i < n - 3; i++) {
            		  out.print(-arr[i + 1] + " ");
            		  out.print(arr[i] + " ");
            		  i++;
            	  }
            	  n--;
            	  if(arr[n - 2] + arr[n - 1] != 0) {
            		  out.print(arr[n] + " ");
            		  out.print(arr[n] + " ");
            		  out.print(-(arr[n- 1] + arr[n - 2]) + " ");
            	  }
            	  else if(arr[n - 1] + arr[n] != 0) {
            		  out.print(-(arr[n] + arr[n - 1]) + " ");
            		  out.print(arr[n - 2] + " ");
            		  out.print(arr[n - 2] + " ");
            	  }
            	  else {
            		  out.print(arr[n - 1] + " ");
            		  out.print(-(arr[n - 2] + arr[n]) + " ");
            		  out.print(arr[n - 1] + " ");
            	  }
              }
              else {
            	  for(int i = 0; i < n ; i++) {
            		  out.print(-arr[i + 1] + " ");
            		  out.print(arr[i] + " ");
            		  i++;
            	  }  
              }
              out.println();
			}
		out.close();
	}
}