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.
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define mod 1000000007
#define mxx 200005
#define inf 2e18
ll dp[100005];
ll power[mxx];
ll factorial[mxx];

bool isPrime(ll n)
{
    if(n<=3)return true;
    else if(n%2==0 || n%3==0)
      return false;
    for(ll i=5;i*i<=n;i=i+6)
      if(n%i==0 || n%(i+2)==0)
         return false;
         return true;
}

ll powm(ll x,ll y)
{
   ll res=1;
   while(y>0)
   {
      if(y&1)
      res=(res*x)%mod;
      x=(x*x)%mod;y>>=1;
   }
return res;
}

ll poww(ll x,ll y)
{
   ll res=1;
   while(y>0)
   {
      if(y&1)
      res=(res*x);
      x=(x*x);y>>=1;
   }
return res;
}

ll mod_inverse(ll a)
{
   return poww(a ,mod-2);
}



void preComputeFactorial() {
    factorial[0]=power[0]=1;
    for(ll i=1; i<mxx; i++) {
        factorial[i]=(factorial[i-1]*i)%mod;
        power[i]=poww(factorial[i],mod-2);

    }
}

ll nCr(ll n, ll r) {
    return (factorial[n]*( (power[r]*power[n-r])%mod) )%mod;
}

///*****solve****** ///


void solve()
{
   ll n,i,j;
   cin>>n;
   ll arr[n];
   stack<ll>s;
   for(i=0;i<n;i++)
      cin>>arr[i];
   if(n&1)
   {
      
      for(j=n-1,i=0;i+2<j;i++,j--)
      {
         ll l=arr[i]*arr[j];
         if(l>0)
         {
            ll lcm=l/(__gcd(arr[i],arr[j]));
          cout<<lcm/arr[i]<<" ";
          s.push(-lcm/arr[j]);
         }
       else
       {
         if(arr[i]<0)
         {
             ll lcm=-l/(__gcd(-arr[i],arr[j]));
            cout<<lcm/arr[i]<<" ";
             s.push(-lcm/arr[j]);
         }
         else
         {
            ll lcm=-l/(__gcd(arr[i],-arr[j]));
            cout<<lcm/arr[i]<<" ";
             s.push(-lcm/arr[j]);
         }
       }
         
      }

      ll c=abs(arr[i]*arr[i+1]*arr[i+2]);
      ll gcd=__gcd(abs(arr[i+2]),__gcd(abs(arr[i]),abs(arr[i+1])));
      cout<<c/(arr[i]*gcd)<<" "<<-(((abs(arr[i+1])/arr[i+1])*(2*c))/(gcd*abs(arr[i+1])))<<" "<<c/(arr[i+2]*gcd)<<" ";
      while(s.size())
      {
         cout<<s.top()<<" ";
         s.pop();
      }
   }
   else
   {
      for(j=n-1,i=0;i<j;i++,j--)
      {
         if(arr[i]*arr[j]>0)
         {
          cout<<arr[j]<<" ";
          s.push(-arr[i]);
         }
       else
       {
         if(arr[i]<0)
         {
            cout<<-arr[j]<<" ";
            s.push(arr[i]);
         }
         else
         {
            cout<<arr[j]<<" ";
            s.push(-arr[i]);
         }
       }
         
      }
       while(s.size())
      {
         cout<<s.top()<<" ";
         s.pop();
      }
   }

   cout<<"\n";
}
 
int main()
{

ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);


ll t;
t=1;
cin>>t;
while(t--)
solve();
return 0;
}