human
PYTHON3 solution for "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.":


 ... What is a Python program to find any such array b!?
assistant
#Here is Python program to find any such array b!
.
 def answer():
    N = int(input())
    a = list(map(int,input().split()))
    m = min(abs(i) for i in a)
    
    b = [1]*N
    tS = 0
    flg = -1
    for i in range(N):
        if abs(a[i]) == m and flg == -1:
            flg = i
            continue
        
        if tS*a[i] < 0  and tS + a[i] != 0:
            b[i] = 1
            tS += a[i]
        elif tS - a[i] != 0:
            b[i] = -1
            tS -= a[i]
        else:
            b[i] = 1
            tS += a[i]
            
    from math import gcd
    
    m_coeff = ((tS*m)//gcd(tS,m))//m
    s_coeff = ((tS*m)//gcd(tS,m))//tS
    
    for i in range(N):
        if i != flg:
            b[i] *= s_coeff
        else:
            b[i] = m_coeff
    if sum(a[i]*b[i] for i in range(N)) != 0:
        b[flg] -= 2*m_coeff
    print(*b)
    return
        
        
    
    
t = int(input())
for _ in range(t):
    answer()