#define _SILENCE_CXX17_C_HEADER_DEPRECATION_WARNING #define _CRT_SECURE_NO_WARNINGS #include using namespace std; namespace FFT { typedef double dbl; struct num { dbl x, y; num() { x = y = 0; } num(dbl x, dbl y) : x(x), y(y) { } }; inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); } inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); } inline num operator*(num a, num b) { return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x); } inline num conj(num a) { return num(a.x, -a.y); } int base = 1; vector roots = { {0, 0}, {1, 0} }; vector rev = { 0, 1 }; const dbl PI = acosl(-1.0); void ensure_base(int nbase) { if (nbase <= base) { return; } rev.resize(1 << nbase); for (int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } roots.resize(1 << nbase); while (base < nbase) { dbl angle = 2 * PI / (1 << (base + 1)); for (int i = 1 << (base - 1); i < (1 << base); i++) { roots[i << 1] = roots[i]; dbl angle_i = angle * (2 * i + 1 - (1 << base)); roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i)); } base++; } } void fft(vector& a, int n = -1) { if (n == -1) { n = a.size(); } assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for (int i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (int k = 1; k < n; k <<= 1) { for (int i = 0; i < n; i += 2 * k) { for (int j = 0; j < k; j++) { num z = a[i + j + k] * roots[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector fa, fb; vector multiply(vector& a, vector& b) { int need = a.size() + b.size() - 1; int nbase = 1; while ((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; if (sz > (int)fa.size()) { fa.resize(sz); } for (int i = 0; i < sz; i++) { int x = (i < (int)a.size() ? a[i] : 0); int y = (i < (int)b.size() ? b[i] : 0); fa[i] = num(x, y); } fft(fa, sz); num r(0, -0.25 / (sz >> 1)); for (int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r; if (i != j) { fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r; } fa[i] = z; } for (int i = 0; i < (sz >> 1); i++) { num A0 = (fa[i] + fa[i + (sz >> 1)]) * num(0.5, 0); num A1 = (fa[i] - fa[i + (sz >> 1)]) * num(0.5, 0) * roots[(sz >> 1) + i]; fa[i] = A0 + A1 * num(0, 1); } fft(fa, sz >> 1); vector res(need); for (int i = 0; i < need; i++) { if (i % 2 == 0) { res[i] = fa[i >> 1].x + 0.5; } else { res[i] = fa[i >> 1].y + 0.5; } } return res; } vector square(const vector& a) { int need = a.size() + a.size() - 1; int nbase = 1; while ((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; if ((sz >> 1) > (int)fa.size()) { fa.resize(sz >> 1); } for (int i = 0; i < (sz >> 1); i++) { int x = (2 * i < (int)a.size() ? a[2 * i] : 0); int y = (2 * i + 1 < (int)a.size() ? a[2 * i + 1] : 0); fa[i] = num(x, y); } fft(fa, sz >> 1); num r(1.0 / (sz >> 1), 0.0); for (int i = 0; i <= (sz >> 2); i++) { int j = ((sz >> 1) - i) & ((sz >> 1) - 1); num fe = (fa[i] + conj(fa[j])) * num(0.5, 0); num fo = (fa[i] - conj(fa[j])) * num(0, -0.5); num aux = fe * fe + fo * fo * roots[(sz >> 1) + i] * roots[(sz >> 1) + i]; num tmp = fe * fo; fa[i] = r * (conj(aux) + num(0, 2) * conj(tmp)); fa[j] = r * (aux + num(0, 2) * tmp); } fft(fa, sz >> 1); vector res(need); for (int i = 0; i < need; i++) { if (i % 2 == 0) { res[i] = fa[i >> 1].x + 0.5; } else { res[i] = fa[i >> 1].y + 0.5; } } return res; } vector multiply_mod(vector& a, vector& b, int m, int eq = 0) { int need = a.size() + b.size() - 1; int nbase = 0; while ((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; if (sz > (int)fa.size()) { fa.resize(sz); } for (int i = 0; i < (int)a.size(); i++) { int x = (a[i] % m + m) % m; fa[i] = num(x & ((1 << 15) - 1), x >> 15); } fill(fa.begin() + a.size(), fa.begin() + sz, num{ 0, 0 }); fft(fa, sz); if (sz > (int) fb.size()) { fb.resize(sz); } if (eq) { copy(fa.begin(), fa.begin() + sz, fb.begin()); } else { for (int i = 0; i < (int)b.size(); i++) { int x = (b[i] % m + m) % m; fb[i] = num(x & ((1 << 15) - 1), x >> 15); } fill(fb.begin() + b.size(), fb.begin() + sz, num{ 0, 0 }); fft(fb, sz); } dbl ratio = 0.25 / sz; num r2(0, -1); num r3(ratio, 0); num r4(0, -ratio); num r5(0, 1); for (int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); num a1 = (fa[i] + conj(fa[j])); num a2 = (fa[i] - conj(fa[j])) * r2; num b1 = (fb[i] + conj(fb[j])) * r3; num b2 = (fb[i] - conj(fb[j])) * r4; if (i != j) { num c1 = (fa[j] + conj(fa[i])); num c2 = (fa[j] - conj(fa[i])) * r2; num d1 = (fb[j] + conj(fb[i])) * r3; num d2 = (fb[j] - conj(fb[i])) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector res(need); for (int i = 0; i < need; i++) { long long aa = fa[i].x + 0.5; long long bb = fb[i].x + 0.5; long long cc = fa[i].y + 0.5; res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m; } return res; } vector square_mod(vector& a, int m) { return multiply_mod(a, a, m, 1); } }; vector isPrime; // true 表示非素数 false 表示是素数 vector prime; // 保存素数 int sieve(int n) { isPrime.resize(n + 1, false); isPrime[0] = isPrime[1] = true; for (int i = 2; i <= n; i++) { if (!isPrime[i]) prime.emplace_back(i); for (int j = 0; j < (int)prime.size() && prime[j] * i <= n; ++j) { isPrime[prime[j] * i] = true; if (!(i % prime[j])) break; } } return (int)prime.size(); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int n; cin >> n; sieve(3 * n + 1); vector a(n + 1, 0), b(n + 1, 0), c(2 * n + 1, 0); for (int i = 2; i <= n; i++) { if (!isPrime[i]) { a[i] = b[i] = 1; c[i * 2] = 1; } } a = FFT::multiply(a, b); a = FFT::multiply(a, b); c = FFT::multiply(c, b); long long res = 0; for (int i = 2; i <= 3 * n; i++) { if (!isPrime[i]) { res += (a[i] - c[i] * 3) / 6; //cout << (a[i] - c[i] * 3) / 6 << " " << i << "\n"; } } cout << res; return 0; }