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;
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2,fma,tune=native")

#define ll long long
#define int ll
#define ull unsigned ll
#define ld long double
#define rep(a) rep1(i,a)
#define rep1(i,a) rep2(i,0,a)
#define rep2(i,b,a) for(int i=(b); i<((int)(a)); i++)
#define rep3(i,b,a) for(int i=(b); i>=((int)(a)); i--)
#define chkmin(a,b) (a=min(a,b))
#define chkmax(a,b) (a=max(a,b))
#define all(a) a.begin(),a.end()
#define pii pair<int,int>
#define pb push_back
//#define inf 1010000000
#define inf 4000000000000000000
#define eps 1e-9
#define sz(a) ((int)a.size())
#define pow2(x) (1ll<<(x))
#define ceiling(a,b) (((a)+(b)-1)/(b))
#define print0(a) cout << (a) << ' '
#define ykh mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#ifdef i_am_noob
#define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__)
template<typename T> void _do(vector<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(unordered_set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(T && x) {cerr << x << endl;}
template<typename T, typename ...S> void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);}
#else
#define bug(...) 826
#endif
template<typename T> void print(T && x) {cout << x << "\n";}
template<typename T, typename... S> void print(T && x, S&&... y) {cout << x << ' ';print(y...);}

const int Mod=1000000007,Mod2=998244353;
const int MOD=Mod;
const int maxn=100005;

//i_am_noob
#define wiwihorz  
int n,a[maxn],b[maxn];

void orzck(){
    cin >> n;
    rep(n) cin >> a[i];
    int g=0;
    rep(n) g=__gcd(g,a[i]);
    g=abs(g);
    rep(n) a[i]/=g;
    rep(n) b[i]=0;
    int x=0;
    rep(n) if(abs(a[i])<10000){
        x=i;
        break;
    }
    rep(n) if(i!=x){
        if(abs(b[x]+a[i])<=10000){
            b[x]+=a[i];
            b[i]+=-a[x];
        }
        else{
            b[x]+=-a[i];
            b[i]+=a[x];
        }
    }
    if(b[x]==0){
        bug(x);
        rep(n) bug(b[i]);
        int y=(x+1)%n;
        if(b[y]>0){
            b[x]+=2*a[y];
            b[y]=-b[y];
        }
        else{
            b[x]+=-2*a[y];
            b[y]=-b[y];
        }
    }
    rep(n) print0(b[i]);
    cout << "\n";
}

signed main(){
    ios_base::sync_with_stdio(0),cin.tie(0);
    #ifdef i_am_noob
    freopen("input1.txt","r",stdin);
    freopen("output1.txt","w",stdout);
    freopen("output2.txt","w",stderr);
    #endif
    cout << fixed << setprecision(15);
    int t;
    #ifdef wiwihorz
    cin >> t;
    #else
    t=1;
    #endif
    while(t--) orzck();
    return 0;
}