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.
// Problem: D. Vupsen, Pupsen and 0
// Contest: Codeforces - Codeforces Round #750 (Div. 2)
// URL: https://codeforces.com/contest/1582/problem/D
// Memory Limit: 256 MB
// Time Limit: 1000 ms


import java.io.*;
import java.util.*;
 
public class Solution
{
	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());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    
    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
     
    // method to return LCM of two numbers
    static long lcm(long a, long b)
    {
        return (a / gcd(a, b)) * b;
    }
    static void swap(long arr[], int i, int j){
    	long temp = arr[i];
    	arr[i] = arr[j];
    	arr[j] = temp;
    }
    
    static long[] getRes(long arr[], int n){
    	long[] res = new long[n];
    	int start = 0;
    	if (n%2==1){
    		int op = 1;
    		start = 3;
    		long a = arr[0]+arr[1];
    		
    		long b = arr[2];
    		if (a==0){
    			op = 2;
    			a = arr[0]+arr[2];
    			b = arr[1];
    			if (a==0){
    				op = 3;
    				a = arr[1]+arr[2];
    				b = arr[0];
    			}
    		}
    		int neg = 0;
    		if (a<0&&b<0){
    			neg = 2;
    			a = -a;
    			b = -b;
    		}
    		else if (a<0||b<0){
    			neg=1;
    			if (a<0){
    				a = -a;
    			}
    			else {
    				b = -b;
    			}
    		}
    		
    		long lc = lcm(a,b);
    		if (neg%2==0){
    			long mulb = -lc/b;
    			long mula = lc/a;
    			res[0] = mula;
    			res[1] = mula;
    			res[2] = mulb;
    		}
    		else {
    			long mulb = lc/b;
    			long mula = lc/a;
    			res[0] = mula;
    			res[1] = mula;
    			res[2] = mulb;
    		}
    		if (op==2){
    			swap(res,2,1);
    		}
    		else if (op==3){
    			// System.out.println("In 3");
    			swap(res,0,2);
    		}
    	}
    	
    	for (int i = start; i<n; i+=2){
    		long a = arr[i];
    		long b= arr[i+1];
    		int neg = 0;
    		if (a<0&&b<0){
    			neg = 2;
    			a = -a;
    			b = -b;
    		}
    		else if (a<0||b<0){
    			neg=1;
    			if (a<0){
    				a = -a;
    			}
    			else {
    				b = -b;
    			}
    		}
    		
    		long lc = lcm(a,b);
    		if (neg%2==0){
    			long mulb = -lc/b;
    			long mula = lc/a;
    			res[i] = mula;
    			res[i+1] = mulb;
    		}
    		else {
    			long mulb = lc/b;
    			long mula = lc/a;
    			res[i] = mula;
    			res[i+1] = mulb;
    		}
    	}
    	return res;
    	
    }
    
    public static void main(String args[]){
        FastReader s = new FastReader();
        int t = s.nextInt();
        while(t-->0){
        	int n = s.nextInt();
        	long arr[] = new long[n];
        	for (int i = 0; i<n; i++){
        		arr[i] = s.nextLong();
        	}
        	long res[] = getRes(arr,n);
        	for (long ele: res){
        		System.out.print(ele+" ");
        	}
        	System.out.println();
        }
    }
}
