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.
/*
        "Everything in the universe is balanced. Every disappointment
                you face in life will be balanced by something good for you!
                        Keep going, never give up."

*/


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

public class Solution {
    public static void main(String[] args) throws java.lang.Exception {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        sc = new FastReader();

        int test = sc.nextInt();
        for (int t = 0; t < test; t++) {
            solve();
        }
        out.close();
    }

    private static void solve() {
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        }

        int[] res = new int[n];
        if (n % 2 == 0) {
            for (int i = 1; i < n; i += 2) {
                res[i] = arr[i - 1];
                res[i - 1] = -arr[i];
            }
        }else {
            for (int i = 4; i < n; i += 2) {
                res[i] = arr[i - 1];
                res[i - 1] = -arr[i];
            }

            if (arr[0] != arr[1]) {
                res[0] = -arr[2];
                res[1] = -arr[2];
                res[2] = arr[0] + arr[1];
            }else {
                res[0] = -arr[1];
                res[2] = -arr[1];
                res[1] = arr[0] + arr[2];
            }
        }

        for (int i = 0; i < n; i++) {
            out.print(res[i] + " ");
        }
        out.println();
    }


    public static FastReader sc;
    public static PrintWriter out;
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer str;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (str == null || !str.hasMoreElements())
            {
                try
                {
                    str = new StringTokenizer(br.readLine());
                }
                catch (IOException  end)
                {
                    end.printStackTrace();
                }
            }
            return str.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 end)
            {
                end.printStackTrace();
            }
            return str;
        }
    }
}