#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--) #define ALL(v) (v).begin(), (v).end() #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin()) #define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin()) using uint = unsigned int; using ll = long long int; using ull = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; template inline bool chmax(T &a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if (a > b) { a = b; return 1; } return 0; } template T ceil(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x > 0 ? x / y : (x - y + 1) / y); } template int popcnt(T x) { return __builtin_popcountll(x); } template int topbit(T x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } template int lowbit(T x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template ostream &operator<<(ostream &os, const pair &p) { os << "P(" << p.first << ", " << p.second << ")"; return os; } template ostream &operator<<(ostream &os, const vector &vec) { os << "{"; for (int i = 0; i < vec.size(); i++) { os << vec[i] << (i + 1 == vec.size() ? "" : ", "); } os << "}"; return os; } template ostream &operator<<(ostream &os, const map &map_var) { os << "{"; for (auto itr = map_var.begin(); itr != map_var.end(); itr++) { os << "(" << itr->first << ", " << itr->second << ")"; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { os << "{"; for (auto itr = set_var.begin(); itr != set_var.end(); itr++) { os << *itr; ++itr; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } #ifdef LOCAL #define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__) #else #define show(...) true #endif template void _show(int i, T name) { cerr << '\n'; } template void _show(int i, const T1 &a, const T2 &b, const T3 &...c) { for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i]; cerr << ":" << b << " "; _show(i + 1, a, c...); } #line 2 "library/Utility/fastio.hpp" #include namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memmove(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(uint &x) { rd_integer(x); } void rd(ull &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d : x) rd(d); } template void rd(vector &x) { for (auto &d : x) rd(d); } void read() {} template void read(H &h, T &...t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c : s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(uint x) { wt_integer(x); } void wt(ull x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&...tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::flush; using fastio::print; using fastio::read; inline void first(bool i = true) { print(i ? "first" : "second"); } inline void Alice(bool i = true) { print(i ? "Alice" : "Bob"); } inline void Takahashi(bool i = true) { print(i ? "Takahashi" : "Aoki"); } inline void yes(bool i = true) { print(i ? "yes" : "no"); } inline void Yes(bool i = true) { print(i ? "Yes" : "No"); } inline void No() { print("No"); } inline void YES(bool i = true) { print(i ? "YES" : "NO"); } inline void NO() { print("NO"); } inline void Yay(bool i = true) { print(i ? "Yay!" : ":("); } inline void Possible(bool i = true) { print(i ? "Possible" : "Impossible"); } inline void POSSIBLE(bool i = true) { print(i ? "POSSIBLE" : "IMPOSSIBLE"); } /** * @brief Fast IO */ #line 3 "sol.cpp" #line 2 "library/Math/sieve.hpp" templatevector sieve(int N){ bitset isp; int n,sq=ceil(sqrt(N)); for(int z=1;z<=5;z+=4){ for(int y=z;y<=sq;y+=6){ for(int x=1;x<=sq and (n=4*x*x+y*y)<=N;++x){ isp[n].flip(); } for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){ isp[n].flip(); } } } for(int z=2;z<=4;z+=2){ for(int y=z;y<=sq;y+=6){ for (int x=1;x<=sq and (n=3*x*x+y*y)<=N;x+=2){ isp[n].flip(); } for(int x=y+1;x<=sq and (n=3*x*x-y*y)<=N;x+=2){ isp[n].flip(); } } } for(int y=3;y<=sq;y+=6){ for(int z=1;z<=2;++z){ for(int x=z;x<=sq and (n=4*x*x+y*y)<=N;x+=3){ isp[n].flip(); } } } for(int n=5;n<=sq;++n)if(isp[n]){ for(int k=n*n;k<=N;k+=n*n){ isp[k]=false; } } isp[2]=isp[3]=true; vector ret; for(int i=2;i<=N;i++)if(isp[i]){ ret.push_back(i); } return ret; } /** * @brief Prime Sieve */ #line 5 "sol.cpp" const int N = 1010101; int mu[N]; ll G(ll L) { if (L < 12) return 0; ll ret = 0; ll SQ=sqrtl(L); ll border = pow(L, .7); { rep(m, 1, SQ + 3) { if (ll(m + 1) * (m * 2 + 1) * 2 > border) break; rep(s, 1, SQ + 1) { if (ll(m + s) * (m * 2 + s) * 2 > border) break; ret += L / (ll(m + s) * (m * 2 + s) * 2); } } } vector ps(SQ + 3); rep(m, 1, SQ + 1) { if (ll(m + 1) * (m * 2 + 1) * 2 > L) break; ps[m] = (sqrt(ll(m) * m + border * 2) - m * 3) / 2; while (border >= ll(m + ps[m]) * (m * 2 + ps[m]) * 2) ps[m]++; chmax(ps[m], 1); } rep(i, 1, ceil(L, border) + 3) { if (border >= L / i) break; ll rb=L/i; ll cur = 0; rep(m, 1, SQ + 1) { if (ll(m + 1) * (m * 2 + 1) * 2 > rb) break; // border<2(m+s)(2m+s)<=L/i ll q; { q = ll(sqrt(ll(m) * m + rb * 2) - m * 3) >> 1; while ((q + m) * (q + m * 2) * 2 <= rb) q++; } cur += q - ps[m]; } ret += cur; } return ret; } int main() { { auto ps = sieve(N); rep(i, 1, N) mu[i] = 1; for (auto &p : ps) { for (int x = p; x < N; x += p) mu[x] *= -1; if (ll(p) * p >= N) continue; for (int x = p * p; x < N; x += p * p) mu[x] = 0; } } ll L; read(L); ll ret = 0; rep(d, 1, sqrtl(L) + 5) if (d & 1) { if (ll(d) * d > L) break; if(mu[d] != 0) ret += (G(L / d / d) - G(L / d / d / 2)) * mu[d]; } print(ret); return 0; }