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.util.*;
import java.lang.*;

public class TaskD {
    public static void  setVal(int[] ans,int[] a,int index,int val,int sign){
        long newVal = a[index]*(long)val;
        if((newVal<0 && sign<0 )|| (newVal>0 && sign>0)){
            ans[index] = val;
        }
        else{
            ans[index] = -1*val;
        }
    }
    public static void solve(FastReader in,PrintWriter out,int nTestCase) {
        int n = in.nextInt();
        int[] a = in.readArray(n);
        int[] ans = new int[n];
        ArrayList<Pair> sortedPairs = new ArrayList<>();
        for(int i=0;i<n;i++){
            sortedPairs.add(new Pair(Math.abs(a[i]),i));
        }
        Collections.sort(sortedPairs);
        int start = 0;
        if(sortedPairs.size()%2==1){
            start = 3;
            long mul = 1;
            for(int i=0;i<3;i++){
                mul = mul*(long)(sortedPairs.get(i).a);
            }
            if((2*sortedPairs.get(1).a*sortedPairs.get(2).a)<0||(sortedPairs.get(2).a*sortedPairs.get(0).a)<0||(sortedPairs.get(1).a*sortedPairs.get(0).a)<0){
                out.println("Wrong");
                return;
            }
            setVal(ans,a,sortedPairs.get(0).b,(int)(2*sortedPairs.get(1).a*sortedPairs.get(2).a),-1);
            setVal(ans,a,sortedPairs.get(1).b,(int)(sortedPairs.get(2).a*sortedPairs.get(0).a),1);
            setVal(ans,a,sortedPairs.get(2).b,(int)(sortedPairs.get(1).a*sortedPairs.get(0).a),1);
        }
        for(int i=start;i<sortedPairs.size();i+=2){
            long mul = (sortedPairs.get(i).a)*(long)(sortedPairs.get(i+1).a);
            setVal(ans,a,sortedPairs.get(i).b,sortedPairs.get(i+1).a,-1);
            setVal(ans,a,sortedPairs.get(i+1).b,sortedPairs.get(i).a,1);
        }
        for(int i:ans) out.print(i+" ");
        out.println();
    }
    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int T = 1;
        T = in.nextInt();
        for(int tt=1;tt<=T;tt++) {
            solve(in,out,tt);
        }
        out.close();
    }
    static final Random random=new Random();
    static void fastSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            int temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    static void fastSort(char[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            char temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    static int gcd(int a, int b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    static class Pair implements Comparable<Pair>{
        int  a;
        int  b;
        public Pair(int  a, int  b) {
            this.a = a;
            this.b = b;
        }
        public int compareTo(Pair o) {
            if(this.a==o.a)
                return (int)(this.b - o.b);
            return (int)(this.a - o.a);
        }
    }
    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;
        }

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

