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.
//package codeforces;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
public class solution{ 
	public static void main(String[] args){
		Scanner s=new Scanner(System.in);
    	PrintWriter out=new PrintWriter(System.out);
    	int t=s.nextInt();
    	for(int tt=0;tt<t;tt++) {
    		int n=s.nextInt();
    		long a[]=new long[n];
    		for(int i=0;i<n;i++) {
    			a[i]=s.nextLong();
    		}
    		if(n%2==0) {
    			for(int i=0;i<n/2;i++) {
    				out.print(-a[n-i-1]+" ");
    			}
    			for(int i=n/2;i<n;i++) {
    				out.print(a[n-i-1]+" ");
    			}
    			out.println();
    		}else {
    			long sum=0;
    			for(int i=0;i<n;i++) {
    				sum+=a[i];
    			}
    			sum-=a[n/2];
    			
    			long f=a[n/2],g=sum;
    			f=-f;
    			for(int i=0;i<n/2;i++) {
    				out.print(f+" ");
    			}
    			out.print(g+" ");
    			for(int i=0;i<n/2;i++) {
    				out.print(f+" ");
    			}
    			out.println();
    		}
    	}
    	s.close();
    	out.close();
    }
	static boolean ispal(String a) {
		for(int i=0;i<a.length()/2;i++) {
			if(a.charAt(i)!=a.charAt(a.length()-i-1)) {
				return false;
			}
		}
		return true;
	}
	static long power(long x, long y, long p)
	  {
	    long res = 1; 
	    x = x % p; 
	    if (x == 0)
	      return 0; 
	    while (y > 0){
	      if ((y & 1) != 0)
	        res = (res * x) % p;
	      x = (x * x) % p;
	    }
	    return res;
	  }
	public static void printb(boolean ans) {
		if(ans) {
			System.out.println("Yes");
		}else {
			System.out.println("No");
		}
	}
	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;
    }
	static long lcm(long a, long b){
	      return (a*b)/(gcd(a,b));
	    }
	static long gcd(long a, long b){
	      if (b == 0)
	        return a;
	      return gcd(b, a % b);
	    }
    static void sort(long [] a) {
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    static void sort(int [] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
    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();
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		boolean nextBoolean() {
			return Boolean.parseBoolean(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());
		}
		long[] readLongArray(int n) {
			long[] a=new long[n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
	}
    static class Pair implements Comparable<Pair>{
    	int a,b ; 
    	Pair(int a,int b){
    		this.a=a;
    		this.b=b;
    	}
    	public int compareTo(Pair o) {
    		return a-o.a;
    	}
    }
}
