#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int ans = INT_MAX;
    int n;
    cin >> n;
    vector<int> arr(n);
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
    }
    if (n % 2 == 0) {
      for (int i = 0; i < n; i++) {
        if (i < n / 2)
          cout << -arr[n - 1 - i] << " ";
        else
          cout << arr[n - 1 - i] << " ";
      }
      cout << "\n";
    } else {
      int a = arr[0];
      int b = arr[1];
      int c = arr[2];
      if (a + b != 0)
        cout << c << " " << c << " " << -(a + b) << " ";
      else if (a + c != 0)
        cout << b << " " << -(a + c) << " " << b << " ";
      else
        cout << -(b + c) << " " << a << " " << a << " ";
      for (int i = 3; i < n; i++) {
        if (i - 3 < (n - 3) / 2)
          cout << -arr[n - 1 - i + 3] << " ";
        else
          cout << arr[n - 1 - i + 3] << " ";
      }
      cout << "\n";
    }
  }
}

### Prompt

Create a solution in Cpp for the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int ans = INT_MAX;
    int n;
    cin >> n;
    vector<int> arr(n);
    for (int i = 0; i < n; i++) {
      cin >> arr[i];
    }
    if (n % 2 == 0) {
      for (int i = 0; i < n; i++) {
        if (i < n / 2)
          cout << -arr[n - 1 - i] << " ";
        else
          cout << arr[n - 1 - i] << " ";
      }
      cout << "\n";
    } else {
      int a = arr[0];
      int b = arr[1];
      int c = arr[2];
      if (a + b != 0)
        cout << c << " " << c << " " << -(a + b) << " ";
      else if (a + c != 0)
        cout << b << " " << -(a + c) << " " << b << " ";
      else
        cout << -(b + c) << " " << a << " " << a << " ";
      for (int i = 3; i < n; i++) {
        if (i - 3 < (n - 3) / 2)
          cout << -arr[n - 1 - i + 3] << " ";
        else
          cout << arr[n - 1 - i + 3] << " ";
      }
      cout << "\n";
    }
  }
}

```