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.

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


t=int(input())
for _ in range(t):
    n=int(input())
    a = list(map(int, input().split()))
    b=[]
    sum=0
    mini=min(a,key=abs)
    idx=a.index(mini)
    for i in range(n):
        if i==idx:
            b.append(0)
            continue
        if a[i]==(sum):
            sum=sum+a[i]
            b.append(1)
        elif a[i]==(-1*sum):
            sum=sum-a[i]
            b.append(-1)
        elif sum>0 and a[i]<0:
            sum=sum+a[i]
            b.append(1)
        elif sum>0 and a[i]>0:
            sum = sum - a[i]
            b.append(-1)
        elif sum < 0 and a[i] > 0:
            sum = sum + a[i]
            b.append(1)
        elif sum < 0 and a[i] < 0:
            sum = sum - a[i]
            b.append(-1)
        elif sum==0:
            sum=sum+a[i]
            b.append(1)
    sum=sum*-1
    rem=sum%mini
    # print(sum,mini,idx,rem,b)
    if rem==0:
        b[idx]=sum//mini
        print(*b)
    else:
        val=mini//gcd(rem,mini)
        b=[(val*b[i]) for i in range(n)]
        sum=sum*val
        b[idx]=sum//mini
        print(*b)
    # check=0
    # # for i in range(n):
    # #     if b[i]>=10**9:
    # #         print("NO")
    # #         break
    # #     check=check+(a[i]*b[i])
    # # if check==0:
    # #     print("YES")
    # # else:
    # #     print("NO")



