human
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.
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python code to find any such array b!
.

#Codeforces handle - "@titanalpha"

from collections import Counter, deque
import math
from random import randint
from bisect import bisect
import sys
import re
import copy

MOD = 1000000007
MAX = sys.maxsize
MIN = -sys.maxsize

value = {}

class get:
    def int():
        return list(map(int,input().split()))
    def str():
        return input().split()
    def float():
        return list(map(float,input().split()))
    def map():
        return map(int,input().split())

def sqrt(x):
    return int(math.sqrt(x))+1

def gcd(*args):
    result = args[0]
    for item in args:
        result = math.gcd(result,item)
    return result

def LCM(a,b):
    return (a*b)//(math.gcd(a,b))

def three(a,b,c):
    if a+b != 0:
        return (c,c,-(a+b))
    elif b+c != 0:
        return (-(b+c),a,a)
    else:
        return (b,-(a+c),b)

def solve():
    n = int(input())
    a = get.int()
    b = [0]*n
    if n%2 == 0:
        for i in range(0,n,2):
            if a[i]*a[i+1] < 0:
                b[i],b[i+1] = abs(a[i+1]), abs(a[i])
            else:
                b[i] = a[i+1]
                b[i+1] = -a[i]
        print(*b)
    else:
        for i in range(0,n-3,2):
            if a[i]*a[i+1] < 0:
                b[i],b[i+1] = abs(a[i+1]), abs(a[i])
            else:
                b[i] = a[i+1]
                b[i+1] = -a[i]
        b[n-3],b[n-2],b[n-1] = three(a[n-3], a[n-2], a[n-1])
        print(*b)
    
                
for _ in range(int(input())):
    solve()