#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; pair, vector> primes_lpf(const int n) { vector primes; primes.reserve(n / 10); vector lpf(n + 1); for (int i = 2; i <= n; i += 2) lpf[i] = 2; for (int i = 3; i <= n; i += 6) lpf[i] = 3; if (2 <= n) primes.push_back(2); if (3 <= n) primes.push_back(3); // 5 * x <= n, x <= floor(n / 5) const int n5 = n / 5; int x = 5; char add_next = 2; for (; x <= n5; x += add_next, add_next ^= 0x2 ^ 4) { int px = lpf[x]; if (px == 0) { lpf[x] = px = x; primes.push_back(x); } for (int i = 2;; ++i) { int q = primes[i]; int y = q * x; if (y > n) break; lpf[y] = q; if (q == px) break; } } for (; x <= n; x += add_next, add_next ^= 0x2 ^ 4) { if (lpf[x] == 0) { lpf[x] = x; primes.push_back(x); } } return {move(primes), move(lpf)}; } constexpr int PSIZE = 1010000; auto [primes, lpf] = primes_lpf(PSIZE); template T isqrt(T x) { assert (x >= 0); if (x < 1 << 24) return sqrt((float)x); else if (x < 1LL << 52) return sqrt(x); else return sqrtl(x); } ll qcount(ll q) { // x 1<=x<=isqrt(q) // 2x-1<[q/x] <=> 2x<=[q/x] <=> 2x<=q/x <=> x<=isqrt(q/2) // (0, x1], (x1, x2] int x1 = isqrt(q / 2), x2 = isqrt(q); // sum rhs // 1+3+...+2x1-1 = x1^2 ll res = (ll)x1 * x1; for (int i = x1 + 1; i <= x2; i++) res += q / i; // sum lhs // 1+2+...+x2 res -= (ll)x2 * (x2 + 1) / 2; return res; } template vector list_quotients(T n) { vector q; int sq = isqrt(n); // floor(n/sq)==sq // iff floor((n-sq^2)/sq)==0 // iff n-sq^2= 1; i--) q.emplace_back(i); return q; } } int main() { ios::sync_with_stdio(false); cin.tie(0); ll N; cin >> N; N /= 2; auto qs = list_quotients(N); const int sq = isqrt(N), sz = qs.size(); auto get_idx = [&](ll x) { int idx = x <= sq ? sz - (int)x : int(N / x) - 1; assert(0 <= idx && idx < sz); assert(qs[idx] == x); return idx; }; VI coeff(sq + 1); coeff[1] = 1; for (int i = 2; i <= sq; i++) { int j = i / lpf[i]; if (lpf[i] != lpf[j]) coeff[i] = -coeff[j]; } // for (int e2 = 0; N >> e2; e2++) { // ll add = 0; // ll n = N >> e2; // for (int i = 1; (ll)i * i <= n; i++) add += coeff[i] * ans_memo[get_idx(n / ((ll)i * i))]; // ans += e2 % 2 == 0 ? add : -add; // } VI mul(sz); for (int i = 1; (ll)i * i <= N; i += 2) { ll v = N / ((ll)i * i); mul[get_idx(v)] += coeff[i]; // ans += coeff[i] * ans_memo[get_idx(v)]; v /= 2; if (v) { // ans -= coeff[i] * ans_memo[get_idx(v)]; mul[get_idx(v)] -= coeff[i]; } } // int cnt = 0; // rep(i, sz) cnt += mul[i] != 0; // cout << cnt <