D. Vupsen, Pupsen and 0
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$\sum_{i=1}^{n}a_i \cdot b_i=0$$$. 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 $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The next $$$2 \cdot t$$$ 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 $$$n$$$ ($$$2 \le n \le 10^5$$$) — the length of the array.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^4 \le a_i \le 10^4$$$, $$$a_i \neq 0$$$) — the elements of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case print $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ — elements of the array $$$b$$$ ($$$|b_1|+|b_2|+\ldots +|b_n| \le 10^9$$$, $$$b_i \neq 0$$$, $$$\sum_{i=1}^{n}a_i \cdot b_i=0$$$).

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, $$$5 \cdot 1 + 5 \cdot (-1)=5-5=0$$$. You could also print $$$3$$$ $$$-3$$$, for example, since $$$5 \cdot 3 + 5 \cdot (-3)=15-15=0$$$

In the second test case, $$$5 \cdot (-1) + (-2) \cdot 5 + 10 \cdot 1 + (-9) \cdot (-1) + 4 \cdot (-1)=-5-10+10+9-4=0$$$.