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.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.StringTokenizer;

public class TaskD {

    public static void main(String[] arg) {
        final FastScanner in = new FastScanner(System.in);
        final PrintWriter out = new PrintWriter(System.out);
        final int T = in.nextInt();
        for (int t = 0; t < T; t++) {
            int n = in.nextInt();
            int[] a = in.readIntArr(n);
            Solution sol = new Solution(n, a);
            int[] b = sol.solution();
            final StringBuilder res = new StringBuilder();
            for (int i = 0; i < b.length; i++) {
                res.append(b[i]).append(' ');
            }
            out.println(res.toString());
        }
        out.close();
        in.close();
    }

    public static class Solution {
        final int n;
        final int[] a;

        public Solution(final int n, final int[] a) {
            this.n = n;
            this.a = a;
        }

        public int[] solution() {
            final long sum = calcSum(a);
            return TaskD.solution(a, sum);
        }

    }

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

    private static Map<Integer, Integer> buildCntMap(final int[] a) {
        final Map<Integer, Integer> cntMap = new HashMap<>();
        for (int i = 0; i < a.length; i++) {
            Integer cnt = cntMap.getOrDefault(a[i], 0);
            cntMap.put(a[i], cnt + 1);
        }
        return cntMap;
    }

    private static int[] solution(final int[] a, final long sum) {
        final Map<Integer, Integer> cntMap = buildCntMap(a);
        final Set<Integer> visited = new HashSet<>();
        for (int i = 0; i < a.length; i++) {
            if (sum - a[i] == 0) {
                continue;
            }
            if (visited.contains(a[i])) {
                continue;
            }
            visited.add(a[i]);
            long gcd = gcd(sum - a[i], a[i]);
            long lcm = (sum - a[i]) * a[i] / gcd;
            long mul1 = lcm / (sum - a[i]);
            long mul2 = lcm / a[i];
            long bSum = mul1 * (a.length - 1) + mul2;
            if (bSum <= 1_000_000_000) {
                int[] b = new int[a.length];
                Arrays.fill(b, (int) mul1);
                b[i] = 0 - (int) mul2;
                return b;
            }
            if (cntMap.get(a[i]) == 1) {
                continue;
            }
            int leftNums = cntMap.get(a[i]) - 1;
//            int removeCnt = 0;
//            while (leftNums > 0 &&
//                    bSum > 1_000_000_000) {
//                removeCnt++;
//                mul2 -= 2 * mul1;
//                bSum = mul1 * (a.length - 1) + mul2;
//            }
            int changeSignCnt = (int) Math.min(mul2 / (2 * mul1), leftNums);
            bSum -= changeSignCnt * 2 * mul1;

            if (bSum <= 1_000_000_000) {
                int[] b = new int[a.length];
                Arrays.fill(b, (int) mul1);
                b[i] = 0 - (int) (mul2);
                for (int j = 0; j <= a.length && changeSignCnt > 0; j++) {
                    if (a[j] == a[i] && j != i) {
                        changeSignCnt--;
                        b[j] *= -1;
                    }
                }
                return b;
            }
        }
        return null;
    }

    public static long calcSum(int a[]) {
        long sum = 0;
        for (int i = 0; i < a.length; i++) {
            sum += a[i];
        }
        return sum;
    }

    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());
        }

        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());
        }

    }
}
