#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vii = vector<pii>;
using vll = vector<pll>;
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long double eps = 1e-9;
const long long mod = 1000000007;
const int MAXN = 200000;
void solve() {
  ll n, small = INT_MAX, index = 0;
  cin >> n;
  ll arr[n];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    cin >> arr[i];
    if (abs(arr[i]) < small) small = abs(arr[i]), index = i;
  }
  ll b[n];
  memset(b, 0, sizeof b);
  ll t = 0;
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    if (i != index) {
      b[i] -= (t / arr[i] / arr[index]) * arr[index];
      if (b[i] == 0) {
        if (t < 0)
          b[i] = arr[index];
        else
          b[i] = -arr[index];
      }
      t += b[i] * arr[i];
    }
  }
  if (t / arr[index] == 0) {
    for (int i = 0, nnnn = (n); i < nnnn; ++i) {
      if (i != index) {
        t -= b[i] * arr[i];
        b[i] += arr[index];
        if (b[i] == 0) b[i] -= 2 * arr[index];
        t += b[i] * arr[i];
        break;
      }
    }
  }
  b[index] = -1 * t / arr[index];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    cout << b[i] << ' ';
  }
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout << setprecision(12) << fixed;
  int t;
  cin >> t;
  while (t--) solve();
}

### 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;
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vl = vector<ll>;
using vii = vector<pii>;
using vll = vector<pll>;
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const long double eps = 1e-9;
const long long mod = 1000000007;
const int MAXN = 200000;
void solve() {
  ll n, small = INT_MAX, index = 0;
  cin >> n;
  ll arr[n];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    cin >> arr[i];
    if (abs(arr[i]) < small) small = abs(arr[i]), index = i;
  }
  ll b[n];
  memset(b, 0, sizeof b);
  ll t = 0;
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    if (i != index) {
      b[i] -= (t / arr[i] / arr[index]) * arr[index];
      if (b[i] == 0) {
        if (t < 0)
          b[i] = arr[index];
        else
          b[i] = -arr[index];
      }
      t += b[i] * arr[i];
    }
  }
  if (t / arr[index] == 0) {
    for (int i = 0, nnnn = (n); i < nnnn; ++i) {
      if (i != index) {
        t -= b[i] * arr[i];
        b[i] += arr[index];
        if (b[i] == 0) b[i] -= 2 * arr[index];
        t += b[i] * arr[i];
        break;
      }
    }
  }
  b[index] = -1 * t / arr[index];
  for (int i = 0, nnnn = (n); i < nnnn; ++i) {
    cout << b[i] << ' ';
  }
  cout << '\n';
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout << setprecision(12) << fixed;
  int t;
  cin >> t;
  while (t--) solve();
}

```