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;
typedef long long ll;
const int maxn = 3e5 + 5;
typedef pair<int, int> pii;
vector<int> p, ans;
void fun() {
    int n = p.size();
    for (int i = 0; i + 1 < n; i += 2) {
        ans.push_back(p[i + 1]);
        ans.push_back(-p[i]);
    }
}
int main() {
    ios::sync_with_stdio(0);
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        p.clear();
        ans.clear();
        for (int i = 1, x; i <= n; i++) {
            cin >> x;
            p.push_back(x);
        }
        if (n % 2) {
            int x = p.back();
            p.pop_back();
            int y = p.back();
            p.pop_back();
            int z = p.back();
            p.pop_back();
            fun();
            int g = __gcd(abs(x), abs(y));
            int c;
            for (c = 1; c <= 10000; c++) {
                if (c * z % g == 0) {
                    break;
                }
            }
            for (int a = -10000; a <= 10000; a++) {
                if ((a * x + c * z) % y == 0) {
                    int b = (-a * x - c * z) / y;
                    if (abs(b) <= 10000) {
                        ans.push_back(c);
                        ans.push_back(b);
                        ans.push_back(a);
                        break;
                    }
                }
            }
        } else {
            fun();
        }
        for (auto v : ans) {
            cout << v << " ";
        }
        cout << endl;
    }
    return 0;
}