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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.*;


 
public class Codeforces {
	
	static int mod=1000000007 ;
	static List<Integer>[] adj;
	static boolean vst[];
	static int dp[];
	public static void main(String[] args) throws Exception {
		PrintWriter out=new PrintWriter(System.out);
		FastScanner fs=new FastScanner();
		int t=fs.nextInt();
		while(t-->0) {
			int n=fs.nextInt();
			int arr[]=new int[n];
			for(int i=0;i<n;i++) arr[i]=fs.nextInt();
		    int minind=-1;
		    int min=Integer.MAX_VALUE;
		    for(int i=0;i<n;i++) {
		    	if(Math.abs(arr[i])<Math.abs(min)) {
		    		min=arr[i];
		    		minind=i;
		    	}
		    }
//			for(int i=0;i<n;i++) {
//				System.out.print(arr[ind[i]]+ " ");
//			}
//			System.out.println();
			long sum=0;
			for(int i=0;i<n;i++) {
				if(i==minind) continue;
				int mul=-1;
				if(i%2!=0) mul=1;
				sum+=arr[i]*mul;
			}
			long ans[]=new long[n];
			if(sum==0) {
				if(minind+1<n) {
					int mul=-1;
					if((minind+1)%2!=0) mul=1;
					sum+=mul*arr[minind+1];
					ans[minind+1]+=mul;
				}
				else {
					int mul=-1;
					if((minind-1)%2!=0) mul=1;
					sum+=mul*arr[minind-1];
					ans[minind-1]+=mul;
				}
			}
			
			long a= Math.abs(sum), b=Math.abs(arr[minind]);
			long lcm=  (a*b)/gcd(a,b);
			long common=-1, diff=-1;
			common= lcm/a;
			boolean p= sum>=0;
			if(p) {
				if(arr[minind]>0) {
					diff= -lcm/b;
				}
				else {
					diff=lcm/b;
				}
			}
			else {
				if(arr[minind]>0) {
					diff=lcm/b;
				}
				else diff= -lcm/b;
			}
			for(int i=0;i<n;i++) {
				if(i==minind) {
					ans[i]=diff;
					continue;
				}
				int mul=-1;
				if(i%2!=0) mul=1;
				ans[i]+= common*mul;
			}
			
			for(int i=0;i<n;i++) {
				out.print(ans[i]+" ");
			}
			out.println();
		}
		out.close();
		
	}
	
	static long pow(long a,long b) {
		if(b<0) return 1;
		long res=1;
		while(b!=0) {
			if((b&1)!=0) {
				res*=a;
				res%=mod;
			}
			a*=a;
			a%=mod;
			b=b>>1;
		}
		return res;
	}
	static long gcd(long  a,long  b) {
		if(b==0) return a;
		return gcd(b,a%b);
	}
	static long nck(int n,int k) {
		if(k>n) return 0;
		long res=1;
		res*=fact(n);
		res%=mod;
		res*=modInv(fact(k));
		res%=mod;
		res*=modInv(fact(n-k)); 
		res%=mod;
		return res;
	}
	static long fact(long n) {
//		return fact[(int)n];
		long res=1;
		for(int i=2;i<=n;i++) {
			res*=i;
			res%=mod;
		}
		return res;
	}
	
	static long modInv(long n) {
		return pow(n,mod-2);
	}
	
	static void sort(int[] a) {
		//suffle
		int n=a.length;
		Random r=new Random();
		for (int i=0; i<a.length; i++) {
			int oi=r.nextInt(n);
			int temp=a[i];
			a[i]=a[oi];
			a[oi]=temp;
		}
		
		//then sort
		Arrays.sort(a);
	}
	
	// Use this to input code since it is faster than a Scanner
	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());
		}
		long[] lreadArray(int n) {
			long a[]=new long[n];
			for(int i=0;i<n;i++) a[i]=nextLong();
			return a;
		}
		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());
		}
	}
 
}