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 random

def gcd(a,b):
 while b: a,b=b,a%b
 return a

def f(n,a):
 if len(set(map(abs,a)))==1:
  return [(n-1)*(a[0].__cmp__(0))]+[(-1)*(a[i].__cmp__(0)) for i in xrange(1,n)]
 r=sorted(zip(a,range(n)), key=lambda (x,y): abs(x), reverse=True); s=0
 for i in range(n):
  if s<=0:
   if r[i][0]>=0: s+=r[i][0]; r[i]=(1,r[i][1])
   else : s-=r[i][0]; r[i]=(-1,r[i][1])
  else:
   if r[i][0]>=0: s-=r[i][0]; r[i]=(-1,r[i][1])
   else: s+=r[i][0]; r[i]=(1,r[i][1])
 t=(s,0)
 r=[x for (x,y) in sorted(r,key=lambda (x,y): y)]
 if s==0: return r
 while abs(t[0])==abs(s): i=random.randint(0,n-1); t=(a[i],i)
 g=gcd(abs(t[0]),abs(s)); c1=t[0]/g; c2=s/g
 for i in xrange(len(r)): r[i]*=c1
 r[t[1]]-=c2
 s2=sum(a[i]*r[i] for i in xrange(n))
 return r



for t in xrange(int(raw_input())):
 n=int(raw_input())
 a=map(int,raw_input().strip().split())
 print ' '.join(map(str,f(n,a)))
