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
from math import factorial, gcd
#from math import comb, perm 	
from collections import Counter, deque, defaultdict
from bisect import bisect_left, bisect_right 
from heapq import heappop, heappush, heapify, nlargest, nsmallest
from itertools import groupby, accumulate
from copy import deepcopy
MOD = 10**9+7
INF = float('inf')

# import io,os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
# input = sys.stdin.buffer.readline
input = sys.stdin.readline
rl = lambda : list(map(int, input().split()))
rs = lambda : sys.stdin.readline().strip()

for _ in range(int(input())):
	n = int(input())
	A = rl()
	res = [0] * n
	s = 0
	if n % 2 == 1:
		if A[0] != A[1]:
			res[0] = -A[2]
			res[1] = A[2]
			res[2] = A[0] - A[1]
		else:
			res[0] = res[1] = A[2]
			res[2] = -2 * A[0]

		s = 3

	for i in range(s, n, 2):
		res[i] = A[i+1]
		res[i+1] = -A[i]

	print(*res)