Chair Game

In file included from /usr/include/c++/11/algorithm:62,
                 from /usr/include/x86_64-linux-gnu/c++/11/bits/stdc++.h:65,
                 from input/code.cpp:1:
/usr/include/c++/11/bits/stl_algo.h: In instantiation of 'void std::shuffle(_RAIter, _RAIter, _UGenerator&&) [with _RAIter = __gnu_cxx::__normal_iterator<long long int*, std::vector<long long int> >; _UGenerator = int (&)() noexcept]':
input/code.cpp:95:16:   required from here
/usr/include/c++/11/bits/stl_algo.h:3750:9: error: 'std::remove_reference<int (&)() noexcept>::type' {aka 'int() noexcept'} is not a class, struct, or union type
 3750 |         __uc_type;
      |         ^~~~~~~~~
/usr/include/c++/11/bits/stl_algo.h:3778:44: error: 'std::remove_reference<int (&)() noexcept>::type' {aka 'int() noexcept'} is not a class, struct, or union type
 3778 |           const pair<__uc_type, __uc_type> __pospos =
      |                                            ^~~~~~~~
/usr/include/c++/11/bits/stl_algo.h:3778:44: err...

#include <bits/stdc++.h>
using namespace std;

// #undef _GLIBCXX_DEBUG                // disable run-time bound checking, etc
// #pragma GCC optimize("Ofast,inline") // Ofast = O3,fast-math,allow-store-data-races,no-protect-parens
// #pragma GCC optimize ("unroll-loops")

// #pragma GCC target("bmi,bmi2,lzcnt,popcnt")                      // bit manipulation
// #pragma GCC target("movbe")                                      // byte swap
// #pragma GCC target("aes,pclmul,rdrnd")                           // encryption
// #pragma GCC target("avx,avx2,f16c,fma,sse3,ssse3,sse4.1,sse4.2") // SIMD

// #include <bits/extc++.h>
// using namespace __gnu_pbds;
// template<class T>using ordered_set = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
// template<class T>using ordered_multiset = tree<T, null_type, less_equal<T>, rb_tree_tag,tree_order_statistics_node_update>;

#define ll long long
#define INF ((ll)(1e9+7))
#define fo(i, n) for(ll i=0;i<((ll)n);i++)
#define deb(x) cout << #x << " = " << (x) << endl;
#define deb2(x, y) cout << #x << " = " << (x) << ", " << #y << " = " << (y) << endl
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define LSOne(S) ((S) & (-S))
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
inline int readint(){ int v = 0; char c; while((c = getchar()) != EOF && c != ' ' && c != '\n'){ v *= 10; v += c - '0'; } return v; }
inline int readintsigned() { int v = 0; int sign = 1; char c = getchar(); if (c == '-') { sign = -1; } else { v += c - '0'; } while ((c = getchar()) != EOF && c != ' ' && c != '\n') { v *= 10; v += c - '0'; } return v * sign; }
inline string readstring() { string s; char c; while ((c = getchar()) != EOF && c != '\n' && c != ' ') { s.push_back(c); } return s; }
template <class result_t=std::chrono::milliseconds,class clock_t=std::chrono::steady_clock,class duration_t = std::chrono::milliseconds>
auto since(std::chrono::time_point<clock_t, duration_t> const& start){return std::chrono::duration_cast<result_t>(clock_t::now() - start);}
typedef pair<int, int> pii;
typedef pair<ll, ll> pl;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpii;
typedef vector<pl> vpl;
typedef vector<vi> vvi;
typedef vector<vl> vvl;
typedef vector<vpii> vvpii;
typedef vector<vpl> vvpl;

vl v;
// vvl memo;
ll n;
 
 

ll best;
vl current;
 
bool check(){
    vl res(n, 0);
    fo(i, n){
        if(res[(i+v[i])%n]){
            if(i>best){
                current = v;
                best = i;
            }
            
            return 0;
        }
        res[(i+v[i])%n] = 1;
    }
    return 1;
}
 
int main(){
    cin.tie(0)->sync_with_stdio(0);
    
 
    ll t;
    cin >> t;
    srand(50);
    while(t--){
        cin >> n;
        v.assign(n, 0);
        // current.assign(n, 0);
        ll currentSum = 0;
 
        fo(i, n){
            cin >> v[i];
            currentSum+=v[i];
        }
        best = -1;
        // deb(currentSum)
        if(currentSum%n != 0){
            cout << "NO\n";
            continue;
        }
        srand(1337);
        shuffle(all(v), rand);
        current = v;

        while(true){
            if(check()){
                break;
            }
            v = current;
            fo(ii, rand()%n) swap(v[best], v[rand()%n]);
        }
        cout << "YES\n";
        fo(i, n) cout << v[i] << " ";
        cout << "\n";
    }
 
    return 0;
}