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 = lambda: sys.stdin.readline().rstrip('\r\n')

import math

inp_vars_int = lambda: map(int, input().split())
inp_list_int = lambda: list(map(int, input().split()))

t = int(input())

for _ in range(t):
    _ = int(input())
    a = inp_list_int()
    n = len(a)
    a_s = sorted(enumerate(a), key = lambda x: x[1])
    min_diff = math.inf
    i_d = None
    for i in range(1, n):
        diff = a_s[i][1] - a_s[i-1][1]
        if  0 < diff < min_diff:
            i_d = i
            min_diff = diff
    cs = 0
    
    if min_diff in (math.inf, 0):
        b = [1] * (n-1) + [1 - n]
    else:
        b = [None for _ in range(len(a))]
        d2, d1 = a_s[i_d][0], a_s[i_d - 1][0]
        for i, ai in enumerate(a):
            if i in(d1, d2):
                continue
            sig = (cs > 0) == (ai > 0)
            bi = (1 - 2 * sig) * min_diff
            b[i] = bi
            cs += bi * ai
        mult = cs // min_diff
        if mult != 0:
            b[d2], b[d1] = -mult, mult
        else:
            a2, a1 = a[d2], a[d1]
            b[d2], b[d1] = a1 * math.gcd(a2 , a1), -a2 * math.gcd(a2 , a1)
    print(*b)
    print(sum(ai * bi for ai, bi in zip(a, b)))