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.*;

public class tank {

    static final FastScanner fs = new FastScanner();

    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int t = fs.nextInt();
        while(t-- > 0) run_case();

        out.close();
    }

    static void run_case() {
        int n = fs.nextInt();
        int[] a = fs.readArray(n);
        int[] b = new int[n];

        if(n % 2 != 0 && n > 3) {
            fn(a, b, 3, n - 1);
        } else if(n % 2 == 0) {
            fn(a, b, 0, n - 1);
        }

        if(n % 2 != 0) {
            l1:
            for (int i = 0; i < 3; i++) {
                for (int j = 0; j < 3; j++) {
                    if(i != j) {
                        if((a[i] < 0 && a[j] < 0) || (a[i] > 0 && a[j] > 0)) {
                            il(a, b, i, j, (3 ^ i ^ j));
                            break l1;
                        }
                    }
                }
            }
        }

        for(int i: b) out.print(i + " ");
        out.println();
    }

    static void il(int[] a, int[] b, int i1, int i2, int i3) {
        if(a[i2] == a[i1]) {
            b[i3] = -a[i2];
            if(a[i3] != (int) -1e4) {
                b[i1] = 1;
                b[i2] = a[i3] - 1;
            } else {
                b[i1] = -1;
                b[i2] = a[i3] + 1;
            }

            return;
        }
        b[i3] = a[i2] - a[i1];
        b[i1] = a[i3];
        b[i2] = -a[i3];
    }

    static void fn(int[] a, int[] b, int st, int en) {
        while(st < en) {
            b[st] = a[en];
            b[en] = -a[st];
            st++;
            en--;
        }
    }

    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();
        }

        String nextLine(){
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return "";
        }

        int nextInt() {
            return Integer.parseInt(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());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}