// #include "rcpl/my_template.hpp" // using namespace std; // // void solve() { // // TODO: Implement // INT(N); // vector d(N, -1); // vector nzi; // REP(i, N - 1) { // printi("?", i, N - 1); // INT(res); // d[i] = res; // if (res != 0) { // nzi.push_back(i); // } // } // if (LEN(nzi) >= 2) { // i64 abc2 = d[nzi[0]] * d[nzi[1]]; // printi("?", nzi[0], nzi[1]); // INT(bc); // abc2 *= bc; // i64 abc = sqrt_floor(abc2); // d[N - 1] = abc / bc; // REP(i, N - 1) d[i] /= d[N - 1]; // i64 ans = 0; // REP(i, N) ans = ans * 10 + d[N - 1 - i]; // printi("!", ans); // return; // } // vector ansv; // REP(k, 1, 10) { // // d[N - 1] = k とできるか // int ok = 1; // REP(i, N - 1) ok &= d[i] % k == 0; // if (ok) ansv.push_back(k); // } // if (LEN(ansv) == 1) { // d[N - 1] = ansv[0]; // REP(i, N - 1) d[i] /= d[N - 1]; // i64 ans = 0; // REP(i, N) ans = ans * 10 + d[N - 1 - i]; // printi("!", ans); // return; // } // printi("!", -1); // return; // } // // int main() { // int T = 1; // // INT(T); // REP(T) solve(); // return 0; // } #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 #ifdef RUTHEN_LOCAL #include #else #define show(x) true #endif // type definition using i64 = long long; using u32 = unsigned int; using u64 = unsigned long long; using f32 = float; using f64 = double; using f128 = long double; template using pque = std::priority_queue; template using pqueg = std::priority_queue, std::greater>; // overload #define overload4(_1, _2, _3, _4, name, ...) name #define overload3(_1, _2, _3, name, ...) name #define overload2(_1, _2, name, ...) name // for loop #define REP1(a) for (long long _ = 0; _ < (a); _++) #define REP2(i, a) for (long long i = 0; i < (a); i++) #define REP3(i, a, b) for (long long i = (a); i < (b); i++) #define REP4(i, a, b, c) for (long long i = (a); i < (b); i += (c)) #define REP(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define RREP1(a) for (long long _ = (a) - 1; _ >= 0; _--) #define RREP2(i, a) for (long long i = (a) - 1; i >= 0; i--) #define RREP3(i, a, b) for (long long i = (b) - 1; i >= (a); i--) #define RREP(...) overload3(__VA_ARGS__, RREP3, RREP2, RREP1)(__VA_ARGS__) #define FORE1(x, a) for (auto&& x : a) #define FORE2(x, y, a) for (auto&& [x, y] : a) #define FORE3(x, y, z, a) for (auto&& [x, y, z] : a) #define FORE(...) overload4(__VA_ARGS__, FORE3, FORE2, FORE1)(__VA_ARGS__) #define FORSUB(t, s) for (long long t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) // function #define ALL(a) (a).begin(), (a).end() #define RALL(a) (a).rbegin(), (a).rend() #define SORT(a) std::sort((a).begin(), (a).end()) #define RSORT(a) std::sort((a).rbegin(), (a).rend()) #define REV(a) std::reverse((a).begin(), (a).end()) #define UNIQUE(a) \ std::sort((a).begin(), (a).end()); \ (a).erase(std::unique((a).begin(), (a).end()), (a).end()) #define LEN(a) (int)((a).size()) #define MIN(a) *std::min_element((a).begin(), (a).end()) #define MAX(a) *std::max_element((a).begin(), (a).end()) #define SUM1(a) std::accumulate((a).begin(), (a).end(), 0LL) #define SUM2(a, x) std::accumulate((a).begin(), (a).end(), (x)) #define SUM(...) overload2(__VA_ARGS__, SUM2, SUM1)(__VA_ARGS__) #define LB(a, x) std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))) #define UB(a, x) std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))) template inline bool chmin(T& a, const U& b) { return (a > T(b) ? a = b, 1 : 0); } template inline bool chmax(T& a, const U& b) { return (a < T(b) ? a = b, 1 : 0); } template inline T floor(const T x, const S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } template inline T ceil(const T x, const S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template std::pair inline divmod(const T x, const S y) { T q = floor(x, y); return {q, x - q * y}; } // 10 ^ n constexpr long long TEN(int n) { return (n == 0) ? 1 : 10LL * TEN(n - 1); } // 1 + 2 + ... + n #define TRI1(n) ((n) * ((n) + 1LL) / 2) // l + (l + 1) + ... + r #define TRI2(l, r) (((l) + (r)) * ((r) - (l) + 1LL) / 2) #define TRI(...) overload2(__VA_ARGS__, TRI2, TRI1)(__VA_ARGS__) // bit operation // bit[i] (= 0 or 1) #define IBIT(bit, i) (((bit) >> (i)) & 1) // (0, 1, 2, 3, 4) -> (0, 1, 3, 7, 15) #define MASK(n) ((1LL << (n)) - 1) #define POW2(n) (1LL << (n)) #if __cplusplus >= 202002L #include #endif // countr_zero // (000, 001, 010, 011, 100) -> (32, 0, 1, 0, 2) #if __cplusplus >= 202002L using std::countr_zero; #else int countr_zero(unsigned int x) { return x == 0 ? 32 : __builtin_ctz(x); } int countr_zero(unsigned long long int x) { return x == 0 ? 64 : __builtin_ctzll(x); } #endif int countr_zero(int x) { return countr_zero((unsigned int)(x)); } int countr_zero(long long int x) { return countr_zero((unsigned long long int)(x)); } // lowbit // (000, 001, 010, 011, 100) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : countr_zero(x)); } int lowbit(unsigned int x) { return (x == 0 ? -1 : countr_zero(x)); } int lowbit(long long int x) { return (x == 0 ? -1 : countr_zero(x)); } int lowbit(unsigned long long int x) { return (x == 0 ? -1 : countr_zero(x)); } #if __cplusplus >= 202002L #include #endif // popcount // (000, 001, 010, 011, 100) -> (0, 1, 1, 2, 1) #if __cplusplus >= 202002L using std::popcount; #else int popcount(unsigned int x) { return __builtin_popcount(x); } int popcount(unsigned long long int x) { return __builtin_popcountll(x); } #endif int popcount(int x) { return popcount((unsigned int)(x)); } int popcount(long long int x) { return popcount((unsigned long long int)(x)); } #if __cplusplus >= 202002L #include #endif // countl_zero // (000, 001, 010, 011, 100) -> (32, 31, 30, 30, 29) #if __cplusplus >= 202002L using std::countl_zero; #else int countl_zero(unsigned int x) { return x == 0 ? 32 : __builtin_clz(x); } int countl_zero(unsigned long long int x) { return x == 0 ? 64 : __builtin_clzll(x); } #endif int countl_zero(int x) { return countl_zero((unsigned int)(x)); } int countl_zero(long long int x) { return countl_zero((unsigned long long int)(x)); } // topbit // (000, 001, 010, 011, 100) -> (-1, 0, 1, 1, 2) int topbit(int x) { return 31 - countl_zero(x); } int topbit(unsigned int x) { return 31 - countl_zero(x); } int topbit(long long int x) { return 63 - countl_zero(x); } int topbit(unsigned long long int x) { return 63 - countl_zero(x); } // binary search (integer) template T bin_search(T ok, T ng, F& f) { // assert(f(ok) and !f(ng)); while ((ok > ng ? ok - ng : ng - ok) > 1) { T md = (ng + ok) >> 1; (f(md) ? ok : ng) = md; } return ok; } // binary search (real number) template T bin_search_real(T ok, T ng, F& f, const int iter = 100) { // assert(f(ok) and !f(ng)); for (int _ = 0; _ < iter; _++) { T md = (ng + ok) / 2; (f(md) ? ok : ng) = md; } return ok; } // floor(sqrt(x)) template constexpr T sqrt_floor(T x) { return T(sqrtl(x)); } // check if [l1, r1) and [l2, r2) intersect template constexpr bool intersect(const T l1, const T r1, const T l2, const T r2) { return std::max(l1, l2) < std::min(r1, r2); } // check if [a.first, a.second) and [b.first, b.second) intersect template constexpr bool intersect(const std::pair& a, const std::pair& b) { return intersect(a.first, a.second, b.first, b.second); } // rotate matrix counterclockwise by pi / 2 template void rot(std::vector>& a) { if ((int)(a.size()) == 0) return; if ((int)(a[0].size()) == 0) return; int n = (int)(a.size()), m = (int)(a[0].size()); std::vector res(m, std::vector(n)); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { res[m - 1 - j][i] = a[i][j]; } } a.swap(res); } // const value constexpr int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1}; constexpr int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1}; // infinity template constexpr T INF = 0; template <> constexpr int INF = 1'000'000'000; // 1e9 template <> constexpr i64 INF = i64(INF) * INF * 2; // 2e18 template <> constexpr u32 INF = INF; // 1e9 template <> constexpr u64 INF = INF; // 2e18 template <> constexpr f32 INF = INF; // 2e18 template <> constexpr f64 INF = INF; // 2e18 template <> constexpr f128 INF = INF; // 2e18 // I/O // input template std::istream& operator>>(std::istream& is, std::vector& v) { for (auto&& i : v) is >> i; return is; } template void in(T&... a) { (std::cin >> ... >> a); } void scan() {} template void scan(Head& head, Tail&... tail) { in(head); scan(tail...); } // input macro #define INT(...) \ int __VA_ARGS__; \ scan(__VA_ARGS__) #define I64(...) \ i64 __VA_ARGS__; \ scan(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ scan(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ scan(__VA_ARGS__) #define F32(...) \ f32 __VA_ARGS__; \ scan(__VA_ARGS__) #define F64(...) \ f64 __VA_ARGS__; \ scan(__VA_ARGS__) #define F128(...) \ f128 __VA_ARGS__; \ scan(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scan(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ scan(__VA_ARGS__) #define VEC(type, name, size) \ std::vector name(size); \ scan(name) #define VEC2(type, name1, name2, size) \ std::vector name1(size), name2(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i]) #define VEC3(type, name1, name2, name3, size) \ std::vector name1(size), name2(size), name3(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i], name3[i]) #define VEC4(type, name1, name2, name3, name4, size) \ std::vector name1(size), name2(size), name3(size), name4(size); \ for (int i = 0; i < size; i++) scan(name1[i], name2[i], name3[i], name4[i]) #define VV(type, name, h, w) \ std::vector name((h), std::vector((w))); \ scan(name) // output template std::ostream& operator<<(std::ostream& os, const std::vector& v) { auto n = v.size(); for (size_t i = 0; i < n; i++) { if (i) os << ' '; os << v[i]; } return os; } template void out(const T&... a) { (std::cout << ... << a); } void print() { out('\n'); } template void print(Head&& head, Tail&&... tail) { out(head); if (sizeof...(Tail)) out(' '); print(tail...); } // for interactive problems void printi() { std::cout << std::endl; } template void printi(Head&& head, Tail&&... tail) { out(head); if (sizeof...(Tail)) out(' '); printi(tail...); } // bool output void YES(bool t = 1) { print(t ? "YES" : "NO"); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void NO(bool t = 1) { YES(!t); } void No(bool t = 1) { Yes(!t); } void no(bool t = 1) { yes(!t); } void POSSIBLE(bool t = 1) { print(t ? "POSSIBLE" : "IMPOSSIBLE"); } void Possible(bool t = 1) { print(t ? "Possible" : "Impossible"); } void possible(bool t = 1) { print(t ? "possible" : "impossible"); } void IMPOSSIBLE(bool t = 1) { POSSIBLE(!t); } void Impossible(bool t = 1) { Possible(!t); } void impossible(bool t = 1) { possible(!t); } void FIRST(bool t = 1) { print(t ? "FIRST" : "SECOND"); } void First(bool t = 1) { print(t ? "First" : "Second"); } void first(bool t = 1) { print(t ? "first" : "second"); } void SECOND(bool t = 1) { FIRST(!t); } void Second(bool t = 1) { First(!t); } void second(bool t = 1) { first(!t); } // I/O speed up struct SetUpIO { SetUpIO() { std::ios::sync_with_stdio(false); std::cin.tie(0); std::cout << std::fixed << std::setprecision(20); } } set_up_io; using namespace std; void solve() { // TODO: Implement INT(N); vector d(N, -1); vector nzi; REP(i, N - 1) { printi("?", i, N - 1); INT(res); d[i] = res; if (res != 0) { nzi.push_back(i); } } if (LEN(nzi) >= 2) { i64 abc2 = d[nzi[0]] * d[nzi[1]]; printi("?", nzi[0], nzi[1]); INT(bc); abc2 *= bc; i64 abc = sqrt_floor(abc2); d[N - 1] = abc / bc; REP(i, N - 1) d[i] /= d[N - 1]; i64 ans = 0; REP(i, N) ans = ans * 10 + d[N - 1 - i]; printi("!", ans); return; } vector ansv; REP(k, 1, 10) { // d[N - 1] = k とできるか int ok = 1; REP(i, N - 1) ok &= d[i] % k == 0; if (ok) ansv.push_back(k); } if (LEN(ansv) == 1) { d[N - 1] = ansv[0]; REP(i, N - 1) d[i] /= d[N - 1]; i64 ans = 0; REP(i, N) ans = ans * 10 + d[N - 1 - i]; printi("!", ans); return; } printi("!", -1); return; } int main() { int T = 1; // INT(T); REP(T) solve(); return 0; }