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 Main {


    public static void main(String[] args) throws IOException {
        StdIn scn = new StdIn();
        int t = scn.nextInt();
        while (t-- > 0) {
            int n = scn.nextInt();
            int[] arr = scn.readIntArray(n);
            int[] ans = new int[n];
            if (n % 2 == 0) {
                for (int i = 0; i < n; i = i + 2) {
                    ans[i] = -arr[i + 1];
                    ans[i + 1] = arr[i];
                }
                scn.printIntArray(ans);
            } else {
                for (int i = 0; i < n - 3; i = i + 2) {
                    ans[i] = -arr[i + 1];
                    ans[i + 1] = arr[i];
                }
                if (arr[n - 1] + arr[n - 2] != 0) {
                    ans[n - 1] = -arr[n - 3];
                    ans[n - 2] = -arr[n - 3];
                    ans[n - 3] = arr[n - 1] + arr[n - 2];
                }else if (arr[n - 2] + arr[n - 3] != 0){
                    ans[n - 2] = -arr[n - 1];
                    ans[n - 3] = -arr[n - 1];
                    ans[n - 1] = arr[n - 2] + arr[n - 3];
                }else{
                    ans[n - 1] = -arr[n - 2];
                    ans[n - 3] = -arr[n - 2];
                    ans[n - 2] = arr[n - 1] + arr[n - 3];
                }
                scn.printIntArray(ans);
            }
        }
    }

    interface Input {

        public String next();

        public String nextLine();

        public int nextInt();

        public long nextLong();

        public double nextDouble();
    }

    static class StdIn implements Input {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public StdIn() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public StdIn(String filename) {
            try {
                din = new DataInputStream(new FileInputStream(filename));
            } catch (Exception e) {
                throw new RuntimeException();
            }
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String next() {
            int c;
            while ((c = read()) != -1 && (c == ' ' || c == ' ' || c == ' ')) ;
            StringBuilder s = new StringBuilder();
            while (c != -1) {
                if (c == ' ' || c == ' ' || c == ' ')
                    break;
                s.append((char) c);
                c = read();
            }
            return s.toString();
        }

        public String nextLine() {
            int c;
            while ((c = read()) != -1 && (c == ' ' || c == ' ' || c == ' ')) ;
            StringBuilder s = new StringBuilder();
            while (c != -1) {
                if (c == ' ' || c == ' ')
                    break;
                s.append((char) c);
                c = read();
            }
            return s.toString();
        }

        public int nextInt() {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long me(long x, long y, long p) {
            long res = 1;
            x = x % p;
            if (x == 0) {
                return 0;
            }
            while (y > 0) {
                if ((y & 1) != 0) {
                    res = (res * x) % p;
                }
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

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

        public long nextLong() {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long[] readLongArray(int n) {
            long[] ar = new long[n];
            for (int i = 0; i < n; ++i)
                ar[i] = nextLong();
            return ar;
        }

        public long gcd(long a, long b) {
            if (b == 0) {
                return a;
            }
            return gcd(b, a % b);
        }

        public int ncr(int N, int r) {
            double ans = 1;
            for (int i = 1; i <= r; i++) {
                ans = ans * (N - r + i) / i;
            }
            return (int) ans;
        }

        public void printLongArray(long[] a) {
            for (int i = 0; i < a.length; i++) {
                System.out.print(a[i] + " ");
            }
            System.out.println();
        }

        public void printIntArray(int[] a) {
            for (int i = 0; i < a.length; i++) {
                System.out.print(a[i] + " ");
            }
            System.out.println();
        }

        public double nextDouble() {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() {
            try {
                if (bufferPointer == bytesRead)
                    fillBuffer();
                return buffer[bufferPointer++];
            } catch (IOException e) {
                throw new RuntimeException();
            }
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }
}