#include <bits/stdc++.h>
using namespace std;
int t, n, a[100005], b[100005], wz[100005];
const long long INF = 1e9;
long long sum;
int jdz(int x) {
  if (x < 0) return -x;
  return x;
}
bool cmp(int x, int y) {
  if (jdz(a[x]) == jdz(a[y])) return a[x] < a[y];
  return jdz(a[x]) < jdz(a[y]);
}
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      wz[i] = i;
      scanf("%d", &a[i]);
    }
    sort(wz + 1, wz + n + 1, cmp);
    if (n & 1) {
      if ((a[wz[2]] + a[wz[3]]) == 0) swap(wz[1], wz[3]);
      b[wz[1]] = a[wz[2]] + a[wz[3]];
      b[wz[2]] = -a[wz[1]];
      b[wz[3]] = -a[wz[1]];
      for (int i = 4; i <= n; i += 2) {
        if (jdz(a[wz[i]]) == jdz(a[wz[i + 1]])) {
          if (a[wz[i]] == a[wz[i + 1]]) {
            b[wz[i]] = 1;
            b[wz[i + 1]] = -1;
          } else {
            b[wz[i]] = 1;
            b[wz[i + 1]] = 1;
          }
        } else {
          b[wz[i]] = -a[wz[i + 1]];
          b[wz[i + 1]] = a[wz[i]];
        }
      }
      sum = 0;
      for (int i = 1; i <= n; i++) {
        sum = sum + jdz(b[i]);
      }
      if (sum > INF) {
        for (int i = 5; i < n; i += 2) {
          if (jdz(a[wz[i]]) == jdz(a[wz[i + 1]])) {
            if (a[wz[i]] == a[wz[i + 1]]) {
              b[wz[i]] = 1;
              b[wz[i + 1]] = -1;
            } else {
              b[wz[i]] = 1;
              b[wz[i + 1]] = 1;
            }
          } else {
            b[wz[i]] = -a[wz[i + 1]];
            b[wz[i + 1]] = a[wz[i]];
          }
        }
        if (jdz(a[wz[4]]) == jdz(a[wz[n]])) {
          if (a[wz[4]] == a[wz[n]]) {
            b[wz[4]] = 1;
            b[wz[n]] = -1;
          } else {
            b[wz[4]] = 1;
            b[wz[n]] = 1;
          }
        } else {
          b[wz[4]] = -a[wz[n]];
          b[wz[n]] = a[wz[4]];
        }
      }
      for (int i = 1; i <= n; i++) printf("%d ", b[i]);
    } else {
      for (int i = 1; i <= n; i += 2) {
        printf("%d %d ", -a[i + 1], a[i]);
      }
    }
    printf("\n");
  }
  return 0;
}

### Prompt

Develop a solution in cpp 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;
int t, n, a[100005], b[100005], wz[100005];
const long long INF = 1e9;
long long sum;
int jdz(int x) {
  if (x < 0) return -x;
  return x;
}
bool cmp(int x, int y) {
  if (jdz(a[x]) == jdz(a[y])) return a[x] < a[y];
  return jdz(a[x]) < jdz(a[y]);
}
int main() {
  scanf("%d", &t);
  while (t--) {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      wz[i] = i;
      scanf("%d", &a[i]);
    }
    sort(wz + 1, wz + n + 1, cmp);
    if (n & 1) {
      if ((a[wz[2]] + a[wz[3]]) == 0) swap(wz[1], wz[3]);
      b[wz[1]] = a[wz[2]] + a[wz[3]];
      b[wz[2]] = -a[wz[1]];
      b[wz[3]] = -a[wz[1]];
      for (int i = 4; i <= n; i += 2) {
        if (jdz(a[wz[i]]) == jdz(a[wz[i + 1]])) {
          if (a[wz[i]] == a[wz[i + 1]]) {
            b[wz[i]] = 1;
            b[wz[i + 1]] = -1;
          } else {
            b[wz[i]] = 1;
            b[wz[i + 1]] = 1;
          }
        } else {
          b[wz[i]] = -a[wz[i + 1]];
          b[wz[i + 1]] = a[wz[i]];
        }
      }
      sum = 0;
      for (int i = 1; i <= n; i++) {
        sum = sum + jdz(b[i]);
      }
      if (sum > INF) {
        for (int i = 5; i < n; i += 2) {
          if (jdz(a[wz[i]]) == jdz(a[wz[i + 1]])) {
            if (a[wz[i]] == a[wz[i + 1]]) {
              b[wz[i]] = 1;
              b[wz[i + 1]] = -1;
            } else {
              b[wz[i]] = 1;
              b[wz[i + 1]] = 1;
            }
          } else {
            b[wz[i]] = -a[wz[i + 1]];
            b[wz[i + 1]] = a[wz[i]];
          }
        }
        if (jdz(a[wz[4]]) == jdz(a[wz[n]])) {
          if (a[wz[4]] == a[wz[n]]) {
            b[wz[4]] = 1;
            b[wz[n]] = -1;
          } else {
            b[wz[4]] = 1;
            b[wz[n]] = 1;
          }
        } else {
          b[wz[4]] = -a[wz[n]];
          b[wz[n]] = a[wz[4]];
        }
      }
      for (int i = 1; i <= n; i++) printf("%d ", b[i]);
    } else {
      for (int i = 1; i <= n; i += 2) {
        printf("%d %d ", -a[i + 1], a[i]);
      }
    }
    printf("\n");
  }
  return 0;
}

```