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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main1582D {
    public static void main(String[] args) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        int t = in.nextInt();
        for (int i = 0; i < t; i++) {
            int n = in.nextInt();
            int[] a = new int[n];
            for (int j = 0; j < n; j++) {
                a[j] = in.nextInt();
            }
            int[] b = solution(a, n);
            for (int j = 0; j < n; j++) {
                out.print(b[j]);
                out.print(" ");
            }
            out.println();
        }

        out.flush();
        out.close();
        in.close();
    }

    private static int[] solution(int[] a, int n) {
        int[] b = new int[n];
        int start = 0;

        if (n % 2 == 1) {
            if (a[0] + a[1] != 0) {
                b[0] = -a[2];
                b[1] = -a[2];
                b[2] = a[0] + a[1];
            } else if (a[0] + a[2] != 0) {
                b[0] = -a[1];
                b[1] = a[0] + a[2];
                b[2] = -a[1];
            } else {
                b[0] = a[1] + a[2];
                b[1] = -a[0];
                b[2] = -a[0];
            }


            int gcd = gcd(b[0], b[2]);
            b[0] /= gcd;
            b[1] /= gcd;
            b[2] /= gcd;
            start = 3;
        } else {
            b[0] = -a[1];
            b[1] = a[0];
            int gcd = gcd(b[0], b[1]);
            b[0] /= gcd;
            b[1] /= gcd;
            start = 2;
        }
        for (int i = start; i < n; i += 2) {
            b[i] = -a[i + 1];
            b[i + 1] = a[i];
        }
        return b;
    }

    private static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    private static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream stream) {
            try {
                br = new BufferedReader(new InputStreamReader(stream));
            } catch (Exception e) {
                e.printStackTrace();
            }
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        int[] readIntArr(int n) {
            int[] result = new int[n];
            for (int i = 0; i < n; i++) {
                result[i] = Integer.parseInt(next());
            }
            return result;
        }

        long[] readLongArr(int n) {
            long[] result = new long[n];
            for (int i = 0; i < n; i++) {
                result[i] = Long.parseLong(next());
            }
            return result;
        }


        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        long nextLong() {
            return Long.parseLong(next());
        }

    }
}
