// line 1 "answer.cpp" #if !__INCLUDE_LEVEL__ #include __FILE__ int main() { ll n; input(n); vector> ans; vl div = divisor(n); repe(d, div) { ans.emplace_back(0, d, n / d); ans.emplace_back(0, n / d, d); ans.emplace_back(d, 0, n / d); ans.emplace_back(n / d, 0, d); ans.emplace_back(n / d, d, 0); ans.emplace_back(d, n / d, 0); } uniq(ans); rep(i, 1, n) rep(j, i, n) { if (i*j > n) break; auto le = [&] (ll k) -> bool { ll cur = i*j + j*k + k*i; return cur <= n; }; ll k = binsearch(0ll, n+1, le); if (k < j) break; if (i*j + j*k + k*i == n) { ans.emplace_back(i, j, k); ans.emplace_back(i, k, j); ans.emplace_back(j, i, k); ans.emplace_back(k, i, j); ans.emplace_back(j, k, i); ans.emplace_back(k, j, i); } } uniq(ans); print(sz(ans)); repe(e, ans) { auto [x,y,z] = e; print(x,y,z); } } #else // line 2 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp" #include #ifndef LOCAL_TEST #pragma GCC target ("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #endif // LOCAL_TEST using namespace std; // shorten typenames using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; using vs = vector; using vvs = vector>; using vvvs = vector>>; template vector> vv(int h, int w, T val = T()) { return vector(h, vector(w, val)); } template vector>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector(h3, val))); } template vector>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector(h4, val)))); } template using priority_queue_min = priority_queue, greater>; // define CONSTANTS constexpr double PI = 3.14159265358979323; constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL; float EPS = 1e-8; double EPSL = 1e-10; template bool eq(const T x, const T y) { return x == y; } template<> bool eq(const double x, const double y) { return (abs(x - y) < EPSL * x || abs(x - y) < EPSL); } template<> bool eq(const float x, const float y) { return abs(x - y) < EPS * x; } template bool neq(const T x, const T y) { return !(eq(x, y)); } template bool ge(const T x, const T y) { return (eq(x, y) || (x > y)); } template bool le(const T x, const T y) { return (eq(x, y) || (x < y)); } template bool gt(const T x, const T y) { return !(le(x, y)); } template bool lt(const T x, const T y) { return !(ge(x, y)); } constexpr int MODINT998244353 = 998244353; constexpr int MODINT1000000007 = 1000000007; // fasten io struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan; // define macros #define all(a) (a).begin(), (a).end() #define sz(x) ((ll)(x).size()) #define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0,1,...,n-1 #define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // i=0,1,...,n-1 #define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // i=s,s+1,...,t-1 #define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // i=s,s+step,..., T max(array& a) { return *max_element(all(a)); }; template T min(array& a) { return *min_element(all(a)); }; template T max(vector& a) { return *max_element(all(a)); }; template T min(vector& a) { return *min_element(all(a)); }; template vector vec_slice(const vector& a, int l, int r) { vector rev; rep(i, l, r) rev.push_back(a[i]); return rev; }; template T sum(vector& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; }; template bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; }; template inline vector& operator--(vector& v) { repe(x, v) --x; return v; } template inline vector& operator++(vector& v) { repe(x, v) ++x; return v; } ll powm(ll a, ll n, ll mod=INFL) { ll res = 1; while (n > 0) { if (n & 1) res = (res * a) % mod; if (n > 1) a = (a * a) % mod; n >>= 1; } return res; } ll sqrtll(ll x) { assert(x >= 0); ll rev = sqrt(x); while(rev * rev > x) --rev; while((rev+1) * (rev+1)<=x) ++rev; return rev; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } /** * @brief std.hpp * @docs docs/std/std.md */ // line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/prime.hpp" bool is_prime(ll n) { using u128 = __uint128_t; vector a_list = {2, 7, 61, 325, 9375, 28178, 450775, 9780504, 1795265022}; if (n == 1) return false; if (n == 2) return true; if (n % 2 == 0) return false; ll r = 0; ll d = n - 1; while (!(d & 1)) { d >>= 1; r++; } ll cnt = 0; repe(a, a_list) { if (a >= n) continue; u128 res = 1; ll di = d; while (di > 0) { if (di & 1) res = (res * a) % n; if (di > 1) a = (a * a) % n; di >>= 1; } if (res == 1) continue; bool valid = false; rep(i, r) { if (res == n - 1) valid = true; res = (res * res) % n; } if (!valid) return false; } return true; } template vector divisor(T n, bool sorted=true) { vector ans(0); for (T i = 1; i <= (T)std::sqrt(n); i++) { if (n % i == 0) { ans.push_back(i); if (i * i != n) ans.push_back(n / i); } } if (sorted) sort(ans.begin(), ans.end()); return ans; }; template vector prime_factor(T n) { vector ans(0); for (T i = 2; i <= (T)std::sqrt(n); i++) { while (n % i == 0) { ans.push_back(i); n /= i; } } if (n != 1) ans.push_back(n); return ans; }; template map prime_factor_c(T n) { map ans; for (T i = 2; i <= (T)std::sqrt(n); i++) { while (n % i == 0) { ans[i] += 1; n /= i; } } if (n != 1) ans[n] += 1; return ans; }; template vector primes(T n) { vector ans(0); if (n < 2) return ans; vector is_primev(n+1, true); is_primev.at(0) = is_primev.at(1) = false; for (T i = 2; i <= (T)std::sqrt(n); i++) { if (!is_primev.at(i)) continue; for (T j = i*2; j <= n; j+=i) is_primev.at(j) = false; } for (T i = 2; i <= n; i++) { if (is_primev.at(i)) ans.push_back(i); } return ans; }; template vector segment_seive(T s, T t) { vector ans(0); if (t < 2 || s < 0 || s >= t) return ans; vector is_prime_small((T)std::sqrt(t)+1, true); vector is_prime_large(t-s, true); for (T i = 2; i <= (T)std::sqrt(t); i++) { if (!is_prime_small.at(i)) continue; for (T j = i*2; j*j < t; j+=i) is_prime_small.at(j) = false; for (T j = max(2*i, ((s+i-1)/i)*i); j < t; j+=i) is_prime_large.at(j-s) = false; } for (T i=0; i < t-s; i++) { if (is_prime_large.at(i) && s+i != 1) ans.push_back(s+i); } return ans; }; /** * @brief prime.hpp * @docs docs/math/prime.md */ // line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/math/binsearch.hpp" //s~eでle(ans) = trueとなる最大のansを返す template T binsearch(T s, T e, F le) { T cmin = s; T cmax = e; while (cmin != cmax) { T p = (cmin + cmax + 1) / 2; if (le(p)) cmin = p; else cmax = p - 1; } return cmin; } //s~eでle(ans) = trueとなる最大のansを返す template double binsearch_double(double s, double e, F le, double eps=1e-10) { double cmin = s; double cmax = e; while (abs(cmax - cmin) > eps * cmax && abs(cmax - cmin) > eps) { double p = (cmin + cmax) / 2; if (le(p)) cmin = p; else cmax = p; } return cmin; } //s~eで高々1つしか極値を持たないfについて極値を与える点を返す template T ternary_search(T s, T e, F f, double eps=1e-10) { T cmin = s; T cmax = e; while (cmax - cmin > (T)3) { T p1 = cmin + max(1, (cmax - cmin) / 3); T p2 = cmax - max(1, (cmax - cmin) / 3); if (f(p1) > f(p2)) cmin = p1; else cmax = p2; } T rev = cmin; auto val = f(cmin); rep(i, 4) { if (chmin(val, f(cmin+i))) rev = cmin + i; } return rev; } //s~eで高々1つしか極値を持たないfについて極値を与える点を返す template double ternary_search_double(double s, double e, F f, double eps=1e-10) { double cmin = s; double cmax = e; while (abs(cmax - cmin) > eps) { double p1 = cmin + (cmax - cmin) / 3; double p2 = cmax - (cmax - cmin) / 3; if (f(p1) > f(p2)) cmin = p1; else cmax = p2; } return cmin; } /** * @brief binsearch.hpp * @docs docs/math/binsearch.md */ // line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp" // overload operators (prototypes) template inline istream& operator>>(istream& is, pair& p); template inline istream& operator>>(istream& is, vector& v); template inline ostream& operator<<(ostream& os, const pair& p); template inline ostream& operator<<(ostream& os, const vector& v); template ostream &operator<<(ostream &os, const map &mp); template ostream &operator<<(ostream &os, const set &st); template ostream &operator<<(ostream &os, const multiset &st); template ostream &operator<<(ostream &os, const unordered_set &st); template ostream &operator<<(ostream &os, queue q); template ostream &operator<<(ostream &os, deque q); template ostream &operator<<(ostream &os, stack st); template ostream &operator<<(ostream &os, priority_queue pq); // overload operators template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repe(x, v) is >> x; return is; } template inline ostream& operator<<(ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template inline ostream& operator<<(ostream& os, const vector& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; } template ostream &operator<<(ostream &os, const map &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const unordered_set &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, queue q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; } template int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; }; template int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) { cout << val << sep; print_sep_end(sep, end, remain...); return 0; }; template int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; }; template void flush() { cout << flush; }; template int print_and_flush(const T &...args) { print(args...); flush(); return 0; }; #define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print template void input(T &a) { cin >> a; }; template void input(T1&a, T2 &...b) { cin >> a; input(b...); }; #ifdef LOCAL_TEST template void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; } template void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) { int scope = 0; for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) { cerr << name[i]; if (name[i] == '(' || name[i] == '{') scope++; if (name[i] == ')' || name[i] == '}') scope--; } cerr << ":" << a << " "; debug_func(i + 1, name, b...); } template void debug_func(int i, const T1 &name, T2 &a, T3 &...b) { int scope = 0; for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) { cerr << name[i]; if (name[i] == '(' || name[i] == '{') scope++; if (name[i] == ')' || name[i] == '}') scope--; } cerr << ":" << a << " "; debug_func(i + 1, name, b...); } #endif #ifndef LOCAL_TEST template void debug_func(T &...) {} template void debug_func(const T &...) {} #endif /** * @brief io.hpp * @docs docs/std/io.md */ // line 46 "answer.cpp" #endif