/** * date : 2023-10-06 22:57:38 * author : Nyaan */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template using minpq = priority_queue, greater>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N, F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } // 返り値の型は入力の T に依存 // i 要素目 : [0, a[i]) template vector> product(const vector &a) { vector> ret; vector v; auto dfs = [&](auto rc, int i) -> void { if (i == (int)a.size()) { ret.push_back(v); return; } for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back(); }; dfs(dfs, 0); return ret; } // F : function(void(T&)), mod を取る操作 // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I, const function &f) { T res = I; for (; n; f(a = a * a), n >>= 1) { if (n & 1) f(res = res * a); } return res; } // T : 整数型のときはオーバーフローに注意する template T Power(T a, long long n, const T &I = T{1}) { return Power(a, n, I, function{[](T &) -> void {}}); } template T Rev(const T &v) { T res = v; reverse(begin(res), end(res)); return res; } template vector Transpose(const vector &v) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { res[j][i] = v[i][j]; } } return res; } template vector Rotate(const vector &v, int clockwise = true) { using U = typename T::value_type; int H = v.size(), W = v[0].size(); vector res(W, T(H, U{})); for (int i = 0; i < H; i++) { for (int j = 0; j < W; j++) { if (clockwise) { res[W - 1 - j][i] = v[i][j]; } else { res[j][H - 1 - i] = v[i][j]; } } } return res; } } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // using namespace std; using namespace std; namespace internal { template using is_broadly_integral = typename conditional_t || is_same_v || is_same_v, true_type, false_type>::type; template using is_broadly_signed = typename conditional_t || is_same_v, true_type, false_type>::type; template using is_broadly_unsigned = typename conditional_t || is_same_v, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template \ constexpr bool x##_v = x::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template \ struct has_##var : false_type {}; \ template \ struct has_##var> : true_type {}; \ template \ constexpr auto has_##var##_v = has_##var::value; #define ENABLE_HAS_VAR(var) \ template \ struct has_##var : false_type {}; \ template \ struct has_##var> : true_type {}; \ template \ constexpr auto has_##var##_v = has_##var::value; } // namespace internal namespace internal { using namespace std; // a mod p template T safe_mod(T a, T p) { a %= p; if constexpr (is_broadly_signed_v) { if (a < 0) a += p; } return a; } // 返り値:pair(g, x) // s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g template pair inv_gcd(T a, T p) { static_assert(is_broadly_signed_v); a = safe_mod(a, p); if (a == 0) return {p, 0}; T b = p, x = 1, y = 0; while (a) { T q = b / a; swap(a, b %= a); swap(x, y -= q * x); } if (y < 0) y += p / b; return {b, y}; } // 返り値 : a^{-1} mod p // gcd(a, p) != 1 が必要 template T inv(T a, T p) { static_assert(is_broadly_signed_v); a = safe_mod(a, p); T b = p, x = 1, y = 0; while (a) { T q = b / a; swap(a, b %= a); swap(x, y -= q * x); } assert(b == 1); return y < 0 ? y + p : y; } // T : 底の型 // U : T*T がオーバーフローしない かつ 指数の型 template T modpow(T a, U n, T p) { a = safe_mod(a, p); T ret = 1 % p; while (n) { if (n & 1) ret = U(ret) * a % p; a = U(a) * a % p; n >>= 1; } return ret; } // 返り値 : pair(rem, mod) // 解なしのときは {0, 0} を返す template pair crt(const vector& r, const vector& m) { static_assert(is_broadly_signed_v); assert(r.size() == m.size()); int n = int(r.size()); T r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); T r1 = safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) swap(r0, r1), swap(m0, m1); if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } auto [g, im] = inv_gcd(m0, m1); T u1 = m1 / g; if ((r1 - r0) % g) return {0, 0}; T x = (r1 - r0) / g % u1 * im % u1; r0 += x * m0; m0 *= u1; if (r0 < 0) r0 += m0; } return {r0, m0}; } } // namespace internal using namespace std; template struct ArbitraryLazyMontgomeryModIntBase { using mint = ArbitraryLazyMontgomeryModIntBase; inline static UInt mod; inline static UInt r; inline static UInt n2; static constexpr int bit_length = sizeof(UInt) * 8; static UInt get_r() { UInt ret = mod; while (mod * ret != 1) ret *= UInt(2) - mod * ret; return ret; } static void set_mod(UInt m) { assert(m < (UInt(1u) << (bit_length - 2))); assert((m & 1) == 1); mod = m, n2 = -ULong(m) % m, r = get_r(); } UInt a; ArbitraryLazyMontgomeryModIntBase() : a(0) {} ArbitraryLazyMontgomeryModIntBase(const Long &b) : a(reduce(ULong(b % mod + mod) * n2)){}; static UInt reduce(const ULong &b) { return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length; } mint &operator+=(const mint &b) { if (Int(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint &operator-=(const mint &b) { if (Int(a -= b.a) < 0) a += 2 * mod; return *this; } mint &operator*=(const mint &b) { a = reduce(ULong(a) * b.a); return *this; } mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } mint operator+(const mint &b) const { return mint(*this) += b; } mint operator-(const mint &b) const { return mint(*this) -= b; } mint operator*(const mint &b) const { return mint(*this) *= b; } mint operator/(const mint &b) const { return mint(*this) /= b; } bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint(0) - mint(*this); } mint operator+() const { return mint(*this); } mint pow(ULong n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul, n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { Long t; is >> t; b = ArbitraryLazyMontgomeryModIntBase(t); return (is); } mint inverse() const { Int x = get(), y = get_mod(), u = 1, v = 0; while (y > 0) { Int t = x / y; swap(x -= t * y, y); swap(u -= t * v, v); } return mint{u}; } UInt get() const { UInt ret = reduce(a); return ret >= mod ? ret - mod : ret; } static UInt get_mod() { return mod; } }; // id に適当な乱数を割り当てて使う template using ArbitraryLazyMontgomeryModInt = ArbitraryLazyMontgomeryModIntBase; template using ArbitraryLazyMontgomeryModInt64bit = ArbitraryLazyMontgomeryModIntBase; namespace fast_factorize { template bool miller_rabin(const T& n, vector ws) { if (n <= 2) return n == 2; if (n % 2 == 0) return false; T d = n - 1; while (d % 2 == 0) d /= 2; U e = 1, rev = n - 1; for (T w : ws) { if (w % n == 0) continue; T t = d; U y = internal::modpow(w, t, n); while (t != n - 1 && y != e && y != rev) y = y * y % n, t *= 2; if (y != rev && t % 2 == 0) return false; } return true; } bool miller_rabin_u64(unsigned long long n) { return miller_rabin( n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}); } template bool miller_rabin(unsigned long long n, vector ws) { if (n <= 2) return n == 2; if (n % 2 == 0) return false; if (mint::get_mod() != n) mint::set_mod(n); unsigned long long d = n - 1; while (~d & 1) d >>= 1; mint e = 1, rev = n - 1; for (unsigned long long w : ws) { if (w % n == 0) continue; unsigned long long t = d; mint y = mint(w).pow(t); while (t != n - 1 && y != e && y != rev) y *= y, t *= 2; if (y != rev && t % 2 == 0) return false; } return true; } bool is_prime(unsigned long long n) { using mint32 = ArbitraryLazyMontgomeryModInt<96229631>; using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>; if (n <= 2) return n == 2; if (n % 2 == 0) return false; if (n < (1uLL << 30)) { return miller_rabin(n, {2, 7, 61}); } else if (n < (1uLL << 62)) { return miller_rabin( n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}); } else { return miller_rabin_u64(n); } } } // namespace fast_factorize using fast_factorize::is_prime; /** * @brief Miller-Rabin primality test */ using namespace Nyaan; ll send(int i, int j) { out("?", i + 1, j + 1); cout.flush(); ini(x); return x; } void answer(vi a, vi b) { out("!", a, b); cout.flush(); exit(0); } void q() { inl(N); if (N == 1) { answer(vi(1, 1), vi(1, 1)); } ll p = N; while (!is_prime(p)) --p; // a_i = p と確定している状況 auto f = [&](int ap, auto send2) -> pair { vi a(N), b(N); a[ap] = p; // kouho : 1 か p なやつ vi kouho; rep(j, N) { b[j] = send2(ap, j) / p; if (b[j] == 1) kouho.push_back(j); } assert(sz(kouho) == 2); int j = kouho[0]; int j2 = kouho[1]; int g = 0; rep1(i, N - 1) { int k = send2(i, j); g = gcd(g, k); if (k % p == 0) k /= p; a[i] = k; } if (g == p) { b[j] = p; } else { b[j2] = p; } return mkp(a, b); }; vi c(N); rep(i, N) c[i] = send(0, i); ll g = 0; each(x, c) g = gcd(g, x); vi a, b; // 1 の候補を特定する if (g == p) { // a 側, a[0] = p で確定 tie(a, b) = f(0, [](int s, int t) { return send(s, t); }); } else { // a[0] != p で確定 // -> c[j] mod p = 0 である j が p で確定 exit(1); int j = 0; while (c[j] % p) j++; tie(b, a) = f(j, [](int s, int t) { return send(t, s); }); } answer(a, b); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }