#include <bits/stdc++.h>
using namespace std;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
void init_code() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
void func() {
  int n;
  cin >> n;
  vector<int> a(n);
  vector<int> b(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  b = a;
  if (n % 2 == 1) {
    if (a[1] + a[2] != 0) {
      b[0] = a[1] + a[2];
      b[1] = -a[0];
      b[2] = -a[0];
    } else if (a[1] + a[0] != 0) {
      b[0] = -a[2];
      b[1] = -a[2];
      b[2] = a[0] + a[1];
    } else {
      b[0] = -a[1];
      b[1] = a[0] + a[2];
      b[2] = -a[1];
    }
    for (int i = 3; i < n; i += 2) {
      b[i] = a[i + 1];
      b[i + 1] = -a[i];
    }
  } else {
    reverse(b.begin(), b.end());
    for (int i = 0; i < n / 2; i++) {
      b[i] = (-1 * b[i]);
    }
  }
  for (int i = 0; i < n; i++) {
    cout << b[i] << " ";
  }
  cout << "\n";
}
int main() {
  init_code();
  double start1 = (double)clock();
  int t = 1;
  cin >> t;
  while (t--) func();
  double stop1 = (double)clock();
  double duration = (stop1 - start1) / CLOCKS_PER_SEC;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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;
void _print(long long t) { cerr << t; }
void _print(int t) { cerr << t; }
void _print(string t) { cerr << t; }
void _print(char t) { cerr << t; }
void _print(long double t) { cerr << t; }
void _print(double t) { cerr << t; }
void _print(unsigned long long t) { cerr << t; }
template <class T, class V>
void _print(pair<T, V> p);
template <class T>
void _print(vector<T> v);
template <class T>
void _print(set<T> v);
template <class T, class V>
void _print(map<T, V> v);
template <class T>
void _print(multiset<T> v);
template <class T, class V>
void _print(pair<T, V> p) {
  cerr << "{";
  _print(p.first);
  cerr << ",";
  _print(p.second);
  cerr << "}";
}
template <class T>
void _print(vector<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(set<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T>
void _print(multiset<T> v) {
  cerr << "[ ";
  for (T i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
template <class T, class V>
void _print(map<T, V> v) {
  cerr << "[ ";
  for (auto i : v) {
    _print(i);
    cerr << " ";
  }
  cerr << "]";
}
void init_code() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
void func() {
  int n;
  cin >> n;
  vector<int> a(n);
  vector<int> b(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  b = a;
  if (n % 2 == 1) {
    if (a[1] + a[2] != 0) {
      b[0] = a[1] + a[2];
      b[1] = -a[0];
      b[2] = -a[0];
    } else if (a[1] + a[0] != 0) {
      b[0] = -a[2];
      b[1] = -a[2];
      b[2] = a[0] + a[1];
    } else {
      b[0] = -a[1];
      b[1] = a[0] + a[2];
      b[2] = -a[1];
    }
    for (int i = 3; i < n; i += 2) {
      b[i] = a[i + 1];
      b[i + 1] = -a[i];
    }
  } else {
    reverse(b.begin(), b.end());
    for (int i = 0; i < n / 2; i++) {
      b[i] = (-1 * b[i]);
    }
  }
  for (int i = 0; i < n; i++) {
    cout << b[i] << " ";
  }
  cout << "\n";
}
int main() {
  init_code();
  double start1 = (double)clock();
  int t = 1;
  cin >> t;
  while (t--) func();
  double stop1 = (double)clock();
  double duration = (stop1 - start1) / CLOCKS_PER_SEC;
}

```