#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; // using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #ifndef LIBRA_OTHER_INT128_H_ #define LIBRA_OTHER_INT128_H_ #include #include constexpr unsigned __int128 toUInt128(const char *s) { unsigned __int128 x = 0; for (; *s; ++s) x = x * 10 + (*s - '0'); return x; } constexpr __int128 toInt128(const char *s) { if (*s == '-') return -toInt128(s + 1); __int128 x = 0; for (; *s; ++s) x = x * 10 + (*s - '0'); return x; } unsigned __int128 inUInt128() { static char buf[41]; scanf("%s", buf); return toUInt128(buf); } __int128 inInt128() { static char buf[41]; scanf("%s", buf); return toInt128(buf); } void out(unsigned __int128 x) { static char buf[41]; int len = 0; do { buf[len++] = '0' + static_cast(x % 10); } while (x /= 10); for (int i = len; --i >= 0; ) putchar(buf[i]); } void out(__int128 x) { if (x < 0) { putchar('-'); out(-static_cast(x)); } else { out(static_cast(x)); } } std::ostream &operator<<(std::ostream &os, unsigned __int128 x) { static char buf[41]; int len = 0; do { buf[len++] = '0' + static_cast(x % 10); } while (x /= 10); for (int i = len; --i >= 0; ) os << buf[i]; return os; } std::ostream &operator<<(std::ostream &os, __int128 x) { if (x < 0) { os << '-' << -static_cast(x); } else { os << static_cast(x); } return os; } #endif // LIBRA_OTHER_INT128_H_ using Int = __int128; // https://oeis.org/A155046 constexpr Int P = toInt128("233806732499933208099"); constexpr Int Q = toInt128("165326326037771920630"); // #{ (a, b) | a + sqrt(2) b <= t } Int solve(Int t) { Int ret = 0; for (Int b = 0; ; ++b) { const Int limA = t - b * P / Q; if (limA < 0) break; ret += (limA + 1); } return ret; } int main() { long long N_; for (; ~scanf("%lld", &N_); ) { const Int N = N_; Int lo = -1, hi = 200'000; assert(solve(hi) >= N); for (; lo + 1 < hi; ) { const Int mid = (lo + hi) / 2; ((solve(mid) < N) ? lo : hi) = mid; } const Int resLo = solve(lo); // cerr<<"lo = "<