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.
#include <bits/stdc++.h>
using namespace std;
template <typename T>
void write(T x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
namespace FastIO {
const int SIZE = 1 << 16;
char buf[SIZE], str[64];
int l = SIZE, r = SIZE;
int read(char *s) {
  while (r) {
    for (; l < r && buf[l] <= ' '; l++)
      ;
    if (l < r) break;
    l = 0, r = int(fread(buf, 1, SIZE, stdin));
  }
  int cur = 0;
  while (r) {
    for (; l < r && buf[l] > ' '; l++) s[cur++] = buf[l];
    if (l < r) break;
    l = 0, r = int(fread(buf, 1, SIZE, stdin));
  }
  s[cur] = '\0';
  return cur;
}
template <typename type>
bool read(type &x, int len = 0, int cur = 0, bool flag = false) {
  if (!(len = read(str))) return false;
  if (str[cur] == '-') flag = true, cur++;
  for (x = 0; cur < len; cur++) x = x * 10 + str[cur] - '0';
  if (flag) x = -x;
  return true;
}
template <typename type>
type read(int len = 0, int cur = 0, bool flag = false, type x = 0) {
  if (!(len = read(str))) return false;
  if (str[cur] == '-') flag = true, cur++;
  for (x = 0; cur < len; cur++) x = x * 10 + str[cur] - '0';
  return flag ? -x : x;
}
}  // namespace FastIO
using FastIO::read;
const int N = 1e5 + 10, MAXN = 5e3 + 10;
int a[N];
int main() {
  int t;
  read(t);
  while (t--) {
    int n;
    read(n);
    map<int, int> M;
    for (int i = 1; i <= n; i++) read(a[i]);
    if (n % 2 == 0) {
      for (int i = 1; i <= n; i += 2) {
        printf("%d %d ", -a[i + 1], a[i]);
      }
    } else {
      for (int i = 1; i <= n - 3; i++) {
        printf("%d %d ", -a[i + 1], a[i]);
      }
      printf("%d %d %d", a[n], a[n], -(a[n - 2] + a[n - 1]));
    }
    printf("\n");
  }
  return 0;
}
