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.
import sys


input = sys.stdin.readline


def gcd(a, b):
    if b == 0:
        return a
    return gcd(b, a%b)


def find_b(arr):
    min_abs = 10**4+1
    idx = -1
    
    for i in range(len(arr)):
        if abs(arr[i]) < abs(min_abs):
            min_abs = arr[i]
            idx = i
    
    b = [0 for _ in range(len(arr))]
    
    v = 0
    for i in range(len(arr)):
        if i == idx:
            continue
        
        g = gcd(min_abs, arr[i])
        
        t1 = -arr[i]//g
        t2 = min_abs//g
        
        if v >= 0:
            if t1 < 0:
                v += t1
                b[i] = t2
            else:
                v -= t1
                b[i] = -t2
        
        else:
            if t1 < 0:
                v -= t1
                b[i] = -t2
            else:
                v += t1
                b[i] = t2
    
    if v == 0:
        min_used = 10**4+1
        min_idx = 0
        for i in range(len(arr)):
            if i == idx:
                continue
            if abs(b[i]) < abs(min_used):
                min_used = b[i]
                min_idx = i
        
        g = gcd(min_abs, arr[min_idx])
        
        t1 = -arr[min_idx]//g
        t2 = min_abs//g
        
        if min_used * t2 < 0:
            v -= t1
            b[min_idx] -= t2
        else:
            v += t1
            b[min_idx] += t2
    
    b[idx] = v
    
    for i in range(len(arr)):
        print(b[i], end=" ")
    print()


if __name__ == "__main__":
    for _ in range(int(input())):
        n = int(input())
        arr = list(map(int, input().split()))
        find_b(arr)
