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.
t = int(input())
for _ in range(t):
    n = int(input())
    l = list(map(int,input().split()))
    smallest = float('inf')
    chosen_index = -1
    for i in range(n):
        if abs(l[i]) < smallest:
            smallest = abs(l[i])
            chosen_index = i
    sum1 = 0
    b = [0 for j in range(n)]
    for i in range(n):
        if i != chosen_index:
            if sum1 <= 0:
                if l[i] > 0:
                    b[i] = smallest
                    sum1 += abs(smallest*l[i])
                else:
                    b[i] = -smallest
                    sum1 += abs(smallest*l[i])
            else:
                if l[i] > 0:
                    b[i] = -smallest
                    sum1 -= abs(smallest*l[i])
                else:
                    b[i] = smallest
                    sum1 -= abs(smallest*l[i])
    if sum1 == 0:
        if chosen_index != 0:
            if b[0] == smallest:
                b[0] = -smallest
            else:
                b[0] = smallest
            sum1 = -2*abs(l[0]*b[0])
            b[chosen_index] = -(sum1//l[chosen_index])
        else:
            if b[-1]*l[-1] > 0:
                sum1 = -2*abs(b[-1]*l[-1])
            else:
                sum1 = 2*abs(b[-1]*l[-1])
            if b[-1] > 0:
                b[-1] = -b[-1]
            else:
                b[-1] = abs(b[-1])
            b[0] = -(sum1//l[0])
    else:
        b[chosen_index] = -(sum1//l[chosen_index])
    print(*b)