// URL : https://yukicoder.me/problems/no/3081 #pragma region optimize // #pragma GCC optimize("Ofast") // #pragma GCC optimize("unroll-loops") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx") #pragma endregion #include using namespace std; // #include #pragma region boost multiprecision // #include // #include // using Bint = boost::multiprecision::cpp_int; // using Bfloat32 = boost::multiprecision::number>; // using Bfloat1024 = boost::multiprecision::number>; #pragma endregion // #define int long long // #define endl '\n' #pragma region TEMPLATE // clang-format off /* TYPE */ typedef long long ll; typedef long double ld; typedef pair pii; typedef pair pll; typedef vector vpii; typedef vector vpll; typedef vector vi; typedef vector vl; typedef vector vst; typedef vector vb; typedef vector vld; typedef vector> vvi; template> using prique = priority_queue, Cmp>; template using prique_r = prique>; /* CONSTANT */ #define ln '\n' const int INF = 1 << 30; const ll INFF = 1LL << 60; const string ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const int MOD = 1e9 + 7; const int MODD = 998244353; const string alphabet = "abcdefghijklmnopqrstuvwxyz"; const double EPS = 1e-9; const ld PI = 3.14159265358979323846264338327950288; const int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1, 0 }; const int dy[] = { 0, 1, 0, -1, -1, -1, 1, 1, 0 }; /* CONTAINER */ #define PB emplace_back #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define SORT(v) sort(ALL(v)) #define RSORT(v) sort(RALL(v)) #define LESS(x, val) (lower_bound(x.begin(), x.end(), val) - x.begin()) #define LEQ(x, val) (upper_bound(x.begin(), x.end(), val) - x.begin()) #define GREATER(x, val) (int)(x).size() - LEQ((x), (val)) #define GEQ(x, val) (int)(x).size() - LESS((x), (val)) #define UNIQUE(v) sort(ALL(v)); (v).erase(unique(ALL(v)), (v).end()) template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a, make_v(ts...)); } template enable_if_t::value != 0> fill_v(U &u, const V... v) { u = U(v...); } template enable_if_t::value == 0> fill_v(U &u, const V... v) { for (auto &e : u) fill_v(e, v...); } /* LOOP */ #define _overload3(_1, _2, _3, name, ...) name #define _REP(i, n) REPI(i, 0, n) #define REPI(i, a, b) for (ll i = (ll)a; i < (ll)b; ++i) #define REP(...) _overload3(__VA_ARGS__, REPI, _REP,)(__VA_ARGS__) #define _RREP(i, n) RREPI(i, n, 0) #define RREPI(i, a, b) for (ll i = (ll)a; i >= (ll)b; --i) #define RREP(...) _overload3(__VA_ARGS__, RREPI, _RREP,)(__VA_ARGS__) #define EACH(e, v) for (auto& e : v) #define PERM(v) sort(ALL(v)); for (bool c##p = true; c##p; c##p = next_permutation(ALL(v))) /* INPUT */ template void SSS(T& t) { cin >> t; } template void SSS(Head&& head, Tail&&... tail) { cin >> head; SSS(tail...); } #define SS(T, ...) T __VA_ARGS__; SSS(__VA_ARGS__); #define SV(T, v, n) vector v(n); for (auto& i : v) cin >> i; #define SVV(T, v, n, m) vector> v(n, vector(m)); for (auto& r : v) for (auto& i : r) cin >> i; /* OUTPUT */ // Yes / No inline int YES(bool x) { cout << (x ? "YES" : "NO") << endl; return 0; } inline int Yes(bool x) { cout << (x ? "Yes" : "No") << endl; return 0; } inline int yes(bool x) { cout << (x ? "yes" : "no") << endl; return 0; } inline int yES(bool x) { cout << (x ? "yES" : "nO") << endl; return 0; } inline int Yay(bool x) { cout << (x ? "Yay!" : ":(") << endl; return 0; } // PROTOTYPE DECLARATION template ostream &operator<<(ostream &os, const pair &j); template ostream &operator<<(ostream &os, const tuple &t); template::value, decltype(declval().begin(), nullptr)> = nullptr> ostream& operator<<(ostream &os, const C &c); template ostream &operator<<(ostream &os, const stack &j); template ostream &operator<<(ostream &os, const queue &j); template ostream &operator<<(ostream &os, const priority_queue &j); // IMPLEMENTATION template ostream &operator<<(ostream &os, const pair &j) { return os << '{' << j.first << ", " << j.second << '}'; } template enable_if_t PRINT_TUPLE(ostream &os, const tuple &t) {} template enable_if_t PRINT_TUPLE(ostream &os, const tuple &t) { os << get(t); if (num + 1 < sizeof...(T)) os << ", "; PRINT_TUPLE(os, t); } template ostream &operator<<(ostream &os, const tuple &t) { PRINT_TUPLE(os << '{', t); return os << '}'; } template::value, decltype(declval().begin(), nullptr)>> ostream& operator<<(ostream &os, const C &c) { os << '{'; for (auto it = begin(c); it != end(c); it++) { if (begin(c) != it) os << ", "; os << *it; } return os << '}'; } template ostream &operator<<(ostream &os, const stack &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top()); return os << d; } template ostream &operator<<(ostream &os, const queue &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_back(c.front()); return os << d; } template ostream &operator<<(ostream &os, const priority_queue &j) { deque d; for (auto c = j; !c.empty(); c.pop()) d.push_front(c.top()); return os << d; } // OUTPUT FUNCTION template int PV(T &v) { int sz = v.size(); for (int i = 0; i < sz; ++i) cout << v[i] << " \n"[i == sz - 1]; return 0; } inline int print() { cout << endl; return 0; } template int print(Head&& head){ cout << head; return print(); } template int print(Head&& head, Tail&&... tail) { cout << head << " "; return print(forward(tail)...); } #ifdef LOCAL inline void dump() { cerr << endl; } template void dump(Head&& head) { cerr << head; dump(); } template void dump(Head&& head, Tail&&... tail) { cerr << head << ", "; dump(forward(tail)...); } #define debug(...) do {cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; dump(__VA_ARGS__); } while (false) #else #define dump(...) #define debug(...) #endif /* OTHER */ #define fi first #define se second #define MP make_pair #define MT make_tuple template inline bool between(T x, A a, B b) { return ((a <= x) && (x < b)); } template inline bool chmax(A &a, const B &b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A &a, const B &b) { if (a > b) { a = b; return true; } return false; } inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } inline ll POW(ll a, ll b) { ll r = 1; do { if (b & 1) r *= a; a *= a; } while (b >>= 1); return r; } struct abracadabra { abracadabra() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(5); }; } ABRACADABRA; // clang-format on #pragma endregion #pragma region string / rollinghash.hpp /** * @brief ローリングハッシュ * @docs docs/string/rollinghash.md */ using hash_type = unsigned long long; template struct RollingHash { vector hsh, pwr; hash_type umod(hash_type n) { return (n % mod + mod) % mod; } RollingHash() {} RollingHash(const string &s) { int sz = (int)s.size(); hsh.assign(sz + 1, 0); pwr.assign(sz + 1, 0); pwr[0] = 1; for (int i = 0; i < sz; ++i) { if (sz > i) hsh[i + 1] = umod(hsh[i] * base + s[i]); pwr[i + 1] = umod(pwr[i] * base); } } // [l, r) hash_type get(int l, int r) { return umod(hsh[r] % mod + mod - hsh[l] * pwr[r - l] % mod); } // h1 <- h2 hash_type join(hash_type h1, hash_type h2, int h2_sz) { return umod(h1 * pwr[h2_sz] + h2); } // [idx, len_s) + [0, idx) hash_type rotate(hash_type idx, int len_s) { return join(get(idx, len_s), get(0, idx), idx); } }; using RH1 = RollingHash<(int)1e9 + 7>; using RH2 = RollingHash<(int)1e9 + 9>; using RH = tuple; using H = tuple; RH init(const string &s) { return make_tuple(RH1(s), RH2(s)); } H get(RH &rh, int l, int r) { return make_tuple(get<0>(rh).get(l, r), get<1>(rh).get(l, r)); } H rotate(RH &rh, int n, int sz) { return make_tuple(get<0>(rh).rotate(n, sz), get<1>(rh).rotate(n, sz)); } #pragma endregion #pragma region datastructure / cumulativesum / cumulativesum.hpp /** * @brief 1次元累積和 * @docs docs/datastructure/cumulativesum/cumulativesum.md */ template struct CumulativeSum { int sz; vector data; CumulativeSum(const vector &v, const T margin = 0) : sz(v.size()), data(1, margin) { for (int i = 0; i < sz; ++i) data.emplace_back(data[i] + v[i]); } T query(const int &l, const int &r) const { if (l >= r) return 0; return data[min(r, sz)] - data[max(l, 0)]; } T operator[](const int &k) const { return query(k, k + 1); } void print() { for (int i = 0; i < sz; ++i) cerr << data[i] << ' '; cerr << endl; } }; #pragma endregion #pragma region math / prime / divisor.hpp /** * @brief Divisor (約数) * @docs docs/math/prime/divisor.md */ vector divisor(const long long n) { vector ret; for (long long i = 1; i * i <= n; ++i) { if (n % i == 0) { ret.emplace_back(i); if (i * i != n) ret.emplace_back(n / i); } } return ret; } #pragma endregion int solve(); signed main() { // int _T; cin >> _T; for (int t = 1; t <= _T; ++t) solve(); } int solve() { SS(int, N); SS(string, S); if (S.find('H') != string::npos) { return print(-1); } int q = 0; EACH (e, S) { if (e == 'Q') q += 1; } if (q == 0) { return print(-1); } if (q == 1) { return print(S); } RH rh = init(S); vector vec(N, 0); REP (i, N) vec[i] = S[i] == 'Q'; CumulativeSum acc(vec); auto div = divisor(N); EACH (d, div) { if (acc.query(0, d) != N / d) continue; set st; for (int i = 0; i < N; i += d) { st.emplace(get(rh, i, i + d)); } if (st.size() != 1) continue; return print(S.substr(0, d)); } print(-1); return 0; }