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 endl "\n"
#define gcd __gcd
#define grt(x) greater<x>
#define mx3 INT32_MAX
#define mn3 INT32_MIN
#define mx6 INT64_MAX
#define mn6 INT64_MIN
#define pi 3.141592653589793238462
#define all(x) (x).begin(), (x).end()
#define mset(x,y) memset(x,y,sizeof(x))
#define setcnt(x) __builtin_popcount(x)
#define setcntll(x) __builtin_popcountll(x)

typedef long long ll;
typedef unsigned long long ull;
typedef long double lld;
 
#ifndef ONLINE_JUDGE
#define debug(x) cerr << #x<<" "; _print(x); cerr << endl;
#else
#define debug(x);
#endif

void _print(ll t) {cerr << t;}
void _print(int t) {cerr << t;}
void _print(string t) {cerr << t;}
void _print(char t) {cerr << t;}
void _print(lld t) {cerr << t;}
void _print(double t) {cerr << t;}
void _print(ull t) {cerr << t;}
template <class T, class V> void _print(pair <T, V> p);
template <class T> void _print(vector <T> v);
template <class T> void _print(set <T> v);
template <class T, class V> void _print(map <T, V> v);
template <class T> void _print(multiset <T> v);
template <class T, class V> void _print(pair <T, V> p) {cerr << "{"; _print(p.first); cerr << ","; _print(p.second); cerr << "}";}
template <class T> void _print(vector <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]\n";}
template <class T> void _print(set <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T> void _print(multiset <T> v) {cerr << "[ "; for (T i : v) {_print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void _print(map <T, V> v) {cerr << "[ "; for (auto i : v) {_print(i); cerr << " ";} cerr << "]";}

const int M = 1000000007;

long long modpow(long long a,long long b){
    long long res=1;
    while(b>0){
        if(b&1)
        res = (res*a)%M;
        a = (a*a)%M;
        b = b>>1;
    }
    return res;
}
long long power(long long a, long long b) {
    long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = res * a;
        a = a * a;
        b >>= 1;
    }
    return res;
}
ll lcm(ll a,ll b){
    return ((a*b)/gcd(a,b));
}

/*-----------------------------------------------------------------------------------------------------*/

void fun(int ans[],pair<int,int> arr[],int n){
    for(int i=0 ; i<n/2 ; i++){
        int x = lcm(arr[i].first,arr[n-1-i].first);
        if(arr[i].first>0 && arr[n-1-i].first>0){
            ans[arr[i].second] = -1*(x/(arr[i].first));
            ans[arr[n-1-i].second] = (x/(arr[n-1-i].first));
        }
        else if(arr[i].first<0 && arr[n-1-i].first<0){
            ans[arr[i].second] = -1*(x/(arr[i].first));
            ans[arr[n-1-i].second] = (x/(arr[n-1-i].first));
        }
        else{
            ans[arr[i].second] = (x/(arr[i].first));
            ans[arr[n-1-i].second] = (x/(arr[n-1-i].first));
        }
    }
}

int main(){
    #ifndef ONLINE_JUDGE
    freopen("Error.txt", "w", stderr);
    #endif
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    /*--------------------------------------------------------------------------------------------------*/

    int t;
    cin>>t;
 
    while(t--){
        int n,i;
        cin>>n;
 
        int arr[n];
 
        for(i=0 ; i<n ; i++){
            cin>>arr[i];
        }
 
        if(!(n%2)){
            for(i=0 ; i<n ; i+=2){
                int x = lcm(arr[i],arr[i+1]);
                if(arr[i]>0 && arr[i+1]>0){
                    cout<<-1*abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
                else if(arr[i]<0 && arr[n-1-i]<0){
                    cout<<-1*abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
                else{
                    cout<<abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
            }
        }
        else{
            int x =lcm(lcm(arr[n-1],arr[n-2]),arr[n-3]);
            vector<int>ans(3);
 
            if(arr[n-1]>0)
            ans[2]=-2*abs(x/(arr[n-1]));
            else
            ans[2] = abs(x/(arr[n-1]));
            
            if(arr[n-2]<0)
            ans[1] = -1*abs(x/(arr[n-2]));
            else
            ans[1] = abs(x/(arr[n-2]));
            
            if(arr[n-3]<0)
            ans[0] = -1*abs(x/(arr[n-3]));
            else
            ans[0] = abs(x/(arr[n-3]));

            for(i=0 ; i<n-3 ; i+=2){
                int x = lcm(arr[i],arr[i+1]);
                if(arr[i]>0 && arr[i+1]>0){
                    cout<<-1*abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
                else if(arr[i]<0 && arr[i+1]<0){
                    cout<<-1*abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
                else{
                    cout<<abs(x/arr[i])<<" "<<abs(x/arr[i+1])<<" ";
                }
            }
            for(i=0 ; i<3 ; i++)
            cout<<ans[i]<<" ";
        }
        cout<<endl;
    }

    return 0;
}

//segment-tree

//exchange-argument ,game-theory

//the net ninja,traversy media,code blocks(arnav gupta),hitesh chaudhary.

//ford fulkerson's algo ,z algo,kmp,rolling hash.