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 VupsenPupsenAnd0 {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        handleMultiTest(br);
    }

    private static void handleMultiTest(BufferedReader br) throws IOException {
        int T = Integer.parseInt(br.readLine());
        for (int i = 0; i < T; i++) {
            handleTest(br);
        }
    }

    private static void handleTest(BufferedReader br) throws IOException {
        int N = Integer.parseInt(br.readLine());
        int[] a = Arrays.stream(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
        evaluate(N, a);
        System.out.println();
    }

    private static void evaluate(int n, int[] a) {
        if (n % 2 == 0) {
            for (int i = 0; i < n; i++) {
                if (i % 2 == 0) {
                    System.out.print(a[i + 1] + " ");
                } else {
                    System.out.print((-1 * a[i - 1]) + " ");
                }
            }
        } else {
            evaluate(n - 3, a);
            if (a[n - 3] + a[n - 2] + a[n - 1] == 0) {
                System.out.print("1 1 1");
            } else if (a[n - 3] + a[n - 2] != 0) {
                System.out.print(a[n - 1] + " " + a[n - 1] + " " + (-1) * (a[n - 3] + a[n - 2]));
            } else if (a[n - 2] + a[n - 1] != 0) {
                System.out.print((-1) * (a[n - 1] + a[n - 2]) + " " + a[n - 3] + " " + a[n - 3]);
            } else {
                System.out.print(a[n - 2] + " " + (-1) * (a[n - 1] + a[n - 3]) + " " + a[n - 2]);
            }
        }
    }
}
