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.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

public class _1582_D {

    private static final FastScanner in = new FastScanner();
    private static final PrintWriter out = new PrintWriter(System.out);
    private static final PrintWriter err = new PrintWriter(System.err);

    public static void solve() {
        int n = in.nextInt();
        int[] a = in.nextIntArray(n);

        int[] b = new int[n];

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

        if (n % 2 == 1) {
            // a[i] * (-a[i+2]) + a[i+1] * (-a[i+2)) + a[i+2] * (a[i] + a[i+1]) == 0
            if (a[n-3] + a[n-2] != 0) {
                b[n-3] = b[n-2] = -a[n-1];
                b[n-1] = a[n-3] + a[n-2];
            } else if (a[n-2] + a[n-1] != 0) {
                b[n-2] = b[n-1] = -a[n-3];
                b[n-3] = a[n-2] + a[n-1];
            } else if (a[n-1] + a[n-3] != 0){
                b[n-1] = b[n-3] = -a[n-2];
                b[n-2] = a[n-1] + a[n-3];
            }
        }

        validate(a, b);

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

    private static void validate(int[] a, int[] b) {
        long sum = 0;
        for (int i = 0; i < a.length; i++) {
            sum += (long)a[i] * b[i];
        }
        assert sum == 0;
    }

    // Boilerplate
    public static void main(String[] args) {
        int t = in.nextInt();
        while (t-- > 0) {
            solve();
        }

        err.close();
        out.close();
    }

    @SuppressWarnings("unused")
    static class FastScanner {

        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        FastScanner() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (!tok.hasMoreElements()) {
                try {
                    tok = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tok.nextToken();
        }

        String nextLine() {
            String line;
            try {
                line = in.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

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

        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        List<Integer> nextIntegerList(int n) {
            ArrayList<Integer> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }

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

        long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        List<Long> nextLongList(int n) {
            ArrayList<Long> list = new ArrayList<>(n);
            for (int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        ArrayList<Integer>[] nextGraph(int n, int m) {
            @SuppressWarnings("unchecked")
            ArrayList<Integer>[] adj = (ArrayList<Integer>[]) new ArrayList[n];

            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }

            for (int i = 0; i < m; i++) {
                int v = nextInt();
                int t = nextInt();
                adj[v - 1].add(t - 1);
                adj[t - 1].add(v - 1);
            }

            return adj;
        }
    }
}