#line 1 "/home/maspy/compro/library/my_template.hpp" #if defined(LOCAL) #include #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vector argsort(const vector &A) { vector ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "/home/maspy/compro/library/other/io2.hpp" #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ long double __VA_ARGS__; \ IN(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void read(int &a) { cin >> a; } void read(long long &a) { cin >> a; } void read(char &a) { cin >> a; } void read(double &a) { cin >> a; } void read(long double &a) { cin >> a; } void read(string &a) { cin >> a; } template void read(pair &p) { read(p.first), read(p.second); } template void read(vector &a) {for(auto &i : a) read(i);} template void read(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &...tail) { read(head); IN(tail...); } template ostream& operator<<(ostream& os, const pair& A) { os << A.fi << " " << A.se; return os; } template ostream& operator<<(ostream& os, const vector& A) { for (size_t i = 0; i < A.size(); i++) { if(i) os << " "; os << A[i]; } return os; } void print() { cout << "\n"; cout.flush(); } template void print(Head&& head, Tail&&... tail) { cout << head; if (sizeof...(Tail)) cout << " "; print(forward(tail)...); } void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 3 "main.cpp" #line 2 "/home/maspy/compro/library/alg/monoid/add.hpp" template struct Monoid_Add { using value_type = X; static constexpr X op(const X &x, const X &y) noexcept { return x + y; } static constexpr X inverse(const X &x) noexcept { return -x; } static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; } static constexpr X unit() { return X(0); } static constexpr bool commute = true; }; #line 3 "/home/maspy/compro/library/ds/fenwicktree/fenwicktree.hpp" template struct FenwickTree { using G = Monoid; using E = typename G::value_type; int n; vector dat; E total; FenwickTree() {} FenwickTree(int n) { build(n); } template FenwickTree(int n, F f) { build(n, f); } FenwickTree(const vc& v) { build(v); } void build(int m) { n = m; dat.assign(m, G::unit()); total = G::unit(); } void build(const vc& v) { build(len(v), [&](int i) -> E { return v[i]; }); } template void build(int m, F f) { n = m; dat.clear(); dat.reserve(n); total = G::unit(); FOR(i, n) { dat.eb(f(i)); } for (int i = 1; i <= n; ++i) { int j = i + (i & -i); if (j <= n) dat[j - 1] = G::op(dat[i - 1], dat[j - 1]); } total = prefix_sum(m); } E prod_all() { return total; } E sum_all() { return total; } E sum(int k) { return prefix_sum(k); } E prod(int k) { return prefix_prod(k); } E prefix_sum(int k) { return prefix_prod(k); } E prefix_prod(int k) { chmin(k, n); E ret = G::unit(); for (; k > 0; k -= k & -k) ret = G::op(ret, dat[k - 1]); return ret; } E sum(int L, int R) { return prod(L, R); } E prod(int L, int R) { chmax(L, 0), chmin(R, n); if (L == 0) return prefix_prod(R); assert(0 <= L && L <= R && R <= n); E pos = G::unit(), neg = G::unit(); while (L < R) { pos = G::op(pos, dat[R - 1]), R -= R & -R; } while (R < L) { neg = G::op(neg, dat[L - 1]), L -= L & -L; } return G::op(pos, G::inverse(neg)); } void add(int k, E x) { multiply(k, x); } void multiply(int k, E x) { static_assert(G::commute); total = G::op(total, x); for (++k; k <= n; k += k & -k) dat[k - 1] = G::op(dat[k - 1], x); } template int max_right(const F check) { assert(check(G::unit())); int i = 0; E s = G::unit(); int k = 1; while (2 * k <= n) k *= 2; while (k) { if (i + k - 1 < len(dat)) { E t = G::op(s, dat[i + k - 1]); if (check(t)) { i += k, s = t; } } k >>= 1; } return i; } // check(i, x) template int max_right_with_index(const F check) { assert(check(0, G::unit())); int i = 0; E s = G::unit(); int k = 1; while (2 * k <= n) k *= 2; while (k) { if (i + k - 1 < len(dat)) { E t = G::op(s, dat[i + k - 1]); if (check(i + k, t)) { i += k, s = t; } } k >>= 1; } return i; } int kth(E k) { return max_right([&k](E x) -> bool { return x <= k; }); } }; #line 2 "/home/maspy/compro/library/seq/factorial_digit_system.hpp" // 右にある小さいやつの個数 [2,0,3,1] → [2,0,1,0] vc to_factorial_digit_system(vc& A) { int N = len(A); for (auto&& x: A) assert(0 <= x && x < N); FenwickTree> bit(N); vc B(N); FOR_R(i, N) B[i] = bit.sum(0, A[i]), bit.add(A[i], 1); return B; } // 右にある小さいやつの個数 [2,0,1,0] → [2,0,3,1] vc from_factorial_digit_system(vc& A) { int N = len(A); for (auto&& x: A) assert(0 <= x && x < N); vc ANS(N); FenwickTree> bit(N, [&](int i) -> int { return 1; }); FOR(i, N) { ANS[i] = bit.kth(A[i]); bit.add(ANS[i], -1); } return ANS; } #line 5 "main.cpp" void solve() { LL(N); vc A(N, 0); vc B(N); FOR(i, N) B[i] = N - 1 - i; auto ask = [&](vc A) -> int { vc Q = from_factorial_digit_system(A); for (auto& x: Q) ++x; print("?", Q); INT(ret); assert(ret != -1); return ret; }; auto out = [&](vc A) -> void { vc Q = from_factorial_digit_system(A); for (auto& x: Q) ++x; print("!", Q); }; if (ask(B) == 1) return out(B); // B>P, A<=P while (1) { vc C(N); FOR(i, N) C[i] = A[i] + B[i]; FOR_R(i, N - 1) { A[i] += A[i + 1] / (N - 1 - i); A[i + 1] %= (N - 1 - i); } int x = 0; FOR(i, N) { x = C[i] + x; C[i] = x / 2; x %= 2; x = x * (N - 1 - i); } if (A == C) break; (ask(C) ? A : B) = C; } out(A); } signed main() { int T = 1; // INT(T); FOR(T) solve(); return 0; }