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.math.*;
import java.util.*;

public class Main {
	static int mod=1000000007;
	static MyScanner sc = new MyScanner();
	static Output out = new Output();
	public static void main(String[] args) {
		int t=sc.nextInt();
		for (int i=0;i<t;i++) {
			solve();
		}
		out.flush();
	}

	public static void solve() {
		int n=sc.nextInt();
		int a[]=sc.nextIntArr(n);
		int b[]=new int[n];
		if(n%2==0) {
			for(int i=0;i<n/2;i++) {
				b[i]=a[n-i-1];
				b[n-i-1]=-a[i];
			}
		}
		else {
			b[n-1]=-1*(a[n-2]+a[n-3]);
			b[n-2]=a[n-1];
			b[n-3]=a[n-1];
			for(int i=0;i<(n-3)/2;i++) {
				b[i]=a[n-i-4];
				b[n-i-4]=-a[i];
			}
		}
		
		for(int i=0;i<n;i++)
			out.print(b[i]+" ");
		out.println();
	}
}
























class Array{
	static void sort(int[] arr){
		mergesort(arr,0,arr.length-1);
	}
	static void sort(int[] arr,int startIndex,int endIndex){
		mergesort(arr,startIndex,endIndex);
	}

	static void mergesort(int[] arr,int b,int e) {
		if(b<e) {
			int m=b+(e-b)/2;
			mergesort(arr,b,m);
			mergesort(arr,m+1,e);
			merge(arr,b,m,e);
		}
		return;	
	}
	static void merge(int[] arr,int b,int m,int e) {
		int len1=m-b+1,len2=e-m;
		int[] l=new int[len1];
		int[] r=new int[len2];
		for(int i=0;i<len1;i++)l[i]=arr[b+i];
		for(int i=0;i<len2;i++)r[i]=arr[m+1+i];
		int i=0,j=0,k=b;
		while(i<len1 && j<len2) {
			if(l[i]<r[j])arr[k++]=l[i++];
			else arr[k++]=r[j++];
		}
		while(i<len1)arr[k++]=l[i++];
		while(j<len2)arr[k++]=r[j++];
		return;
	}
	
	//2d sort
//	static void sort(int[][] arr){
//		mergesort(arr,0,arr.length-1);
//	}
//	static void sort(int[][] arr,int startIndex,int endIndex){
//		mergesort(arr,startIndex,endIndex);
//	}
//
//	static void mergesort(int[][] arr,int b,int e) {
//		if(b<e) {
//			int m=b+(e-b)/2;
//			mergesort(arr,b,m);
//			mergesort(arr,m+1,e);
//			merge(arr,b,m,e);
//		}
//		return;	
//	}
//	static void merge(int[][] arr,int b,int m,int e) {
//		int len1=m-b+1,len2=e-m;
//		int[][] l=new int[len1][2];
//		int[][] r=new int[len2][2];
//		for(int i=0;i<len1;i++) {
//			l[i][0]=arr[b+i][0];
//			l[i][1]=arr[b+i][1];
//		}
//		for(int i=0;i<len2;i++) {
//			r[i][0]=arr[m+1+i][0];
//			r[i][1]=arr[m+1+i][1];
//		}
//		int i=0,j=0,k=b;
//		while(i<len1 && j<len2) {
//			if(l[i][0]<r[j][0]) {
//				arr[k++][0]=l[i++][0];
//				arr[k-1][1]=l[i-1][1];
//			}
//			else {
//				arr[k++][0]=r[j++][0];
//				arr[k-1][1]=r[j-1][1];
//			}
//		}
//		while(i<len1) {
//			arr[k++][0]=l[i++][0];
//			arr[k-1][1]=l[i-1][1];
//		}
//		while(j<len2) {
//			arr[k++][0]=r[j++][0];
//			arr[k-1][1]=r[j-1][1];
//		}
//		return;
//	}
	
}
class MyScanner {

	BufferedReader br;
	StringTokenizer st;

	public MyScanner() {
		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;
	}

	public int[] nextIntArr(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArr(int n) {
		long a[] = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArr(int n) {
		double a[] = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public String[] nextArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public String[] nextLineArr(int n) {
		String a[] = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLine();
		return a;
	}
}

class Output {
	BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	public void print() {}
	public void println() {
		try {
			out.write("\n");
		} catch (Exception e) {}
	}
	public void print(Object s) {
		try {
			out.write(s + "");
		} catch (Exception e) {}
	}
	public void println(Object s) {
		try {
			out.write(s + "\n");
		} catch (Exception e) {}
	}
	public void flush() {
		try {
			out.flush();
		} catch (Exception e) {}
	}
}