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.
// Generated by Code Flattener.
// https://plugins.jetbrains.com/plugin/9979-idea-code-flattener

import java.io.*;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) {
        Solution solution = new ASolution();
        boolean local = System.getProperty("ONLINE_JUDGE") == null && !solution.isInteractive();
        String input = local ? "input.txt" : null;
        solution.in = new MyScanner(input);
        solution.out = MyWriter.of(null);
        solution.bm = new Benchmark();
        solution.al = new Algorithm();
        solution.run();
        solution.close();
    }

    private abstract static class Solution {
        public MyScanner in;
        public MyWriter out;
        public Benchmark bm;
        public Algorithm al;

        public void init() {
        }

        public abstract void solve();

        protected boolean isMultiTest() {
            return true;
        }

        public void run() {
            init();
            if (isMultiTest()) {
                int t = in.nextInt();
                for (int i = 0; i < t; i++) {
                    solve();
                }
            } else {
                solve();
            }
        }

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

        public boolean isInteractive() {
            return false;
        }
    }

    private static class ASolution extends Solution {
        int get(int x, int y, boolean plus) {
            if (y < 0 == plus == x < 0) return x;
            else return -x;
        }

        public void solve() {
            int n = in.nextInt();
            int[] a = in.nextInts(n);
            int[] b = new int[n];
            for (int i = 0; i < (n % 2 == 0 ? n : n - 3); i += 2) {
                b[i] = get(a[i + 1], a[i], true);
                b[i + 1] = get(a[i], a[i + 1], false);
            }
            if (n % 2 == 1) {
                int tmp = Math.abs(a[n - 3]) - Math.abs(a[n - 2]);
                if (tmp != 0) {
                    b[n - 3] = get(a[n - 1], a[n - 3], true);
                    b[n - 2] = get(a[n - 1], a[n - 2], false);
                    b[n - 1] = get(tmp, a[n - 1], tmp < 0);
                } else {
                    int tmp2 = Math.abs(a[n - 1]);
                    int bn3;
                    int bn2;
                    if (tmp2 != 1) {
                        bn3 = tmp2 - 1;
                        bn2 = 1;
                    } else {
                        bn3 = 2;
                        bn2 = -1;
                    }
                    b[n - 3] = get(bn3, a[n - 3], true);
                    b[n - 2] = get(bn2, a[n - 2], bn2 > 0);
                    b[n - 1] = get(a[n - 3], a[n - 1], false);

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

    private static class MyScanner {
        private final BufferedReader br;
        private StringTokenizer st;

        public MyScanner(String fileName) {
            if (fileName != null) {
                try {
                    File file = new File(getClass().getClassLoader().getResource(fileName).getFile());
                    br = new BufferedReader(new FileReader(file));
                } catch (FileNotFoundException e) {
                    throw new RuntimeException(e);
                }
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

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

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

        public String nextLine() {
            try {
                String line = br.readLine();
                if (line == null) {
                    throw new RuntimeException("empty line");
                }
                st = null;
                return line;
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }

    private static class Benchmark {
    }

    private static class Algorithm {
    }

    private static class MyWriter extends PrintWriter {
        public static MyWriter of(String fileName) {
            if (fileName != null) {
                try {
                    return new MyWriter(new FileWriter(fileName));
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            } else {
                return new MyWriter(new BufferedOutputStream(System.out));
            }
        }

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

        public MyWriter(OutputStream out) {
            super(out);
        }
    }
}