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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DVupsenPupsenAnd0 solver = new DVupsenPupsenAnd0();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class DVupsenPupsenAnd0 {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            var a = in.readIntArray(n);

            var b = new int[n];
            if (n % 2 == 0) {
                for (int i = 0; i < n; i += 2) {
                    b[i] = -a[i + 1];
                    b[i + 1] = a[i];
                }
                out.println(b);
                return;
            }

            for (int i = 0; i + 1 < n - 3; i += 2) {
                b[i] = -a[i + 1];
                b[i + 1] = a[i];
            }

            var coef = new int[3];
            NumberTheory.extendedEuclideanAlgo(a[n - 3], a[n - 2], coef);
//		if (!isCorrect(a[n-3], a[n-2], coef)) {
//			for (int i: new int[]{-1, 1}) {
//				boolean ok = false;
//				for (int j: new int[]{-1, 1}) {
//					if (a[n - 3] * i * coef[0] + a[n - 2] * j * coef[1] == coef[2]) {
//						coef[0] = coef[0] * i;
//						coef[1] *= j;
//						ok = true;
//						break;
//					}
//				}
//				if (ok) break;
//			}
//		}
            int c = a[n - 1];
            b[n - 3] = coef[1] * c;
            b[n - 2] = coef[2] * c;
            b[n - 1] = -coef[0];

            out.println(b);

        }

    }

    static class NumberTheory {
        public static void extendedEuclideanAlgo(int a, int b, int[] res) {
            if (b == 0) {
                res[0] = a;
                res[1] = 1;
                res[2] = 0;
                return;
            }
            extendedEuclideanAlgo(b, a % b, res);
            int temp = res[2];
            res[2] = res[1] - a / b * res[2];
            res[1] = temp;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void println(int[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i > 0) print(' ');
                print(array[i]);
            }
            println();
        }

        public void close() {
            super.close();
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = readLine();
                    if (line == null) continue;
                    tokenizer = new StringTokenizer(line);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public int[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++)
                array[i] = nextInt();
//        IntStream.generate(this::nextInt).limit(size).toArray();
            return array;
        }

    }
}

