#line 1 "verify/number-theory/LC_factorize.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (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())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"
#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;
template <class T, class S = T>
S SUM(const vector<T>& a) {
return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
if (!a || a > b) {
a = b;
return true;
}
return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
if (!a || a < b) {
a = b;
return true;
}
return false;
}
template <class T>
int popcnt(T x) {
return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"
#line 2 "template/inout.hpp"
struct Fast {
Fast() {
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} fast;
ostream& operator<<(ostream& os, __uint128_t x) {
char buf[40];
size_t k = 0;
while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
if (k == 0) buf[k++] = '0';
while (k) os << buf[--k];
return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
for (auto& v : a) is >> v;
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
for (auto it = a.begin(); it != a.end();) {
os << *it;
if (++it != a.end()) os << " ";
}
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
os << "{";
for (auto it = st.begin(); it != st.end();) {
os << *it;
if (++it != st.end()) os << ",";
}
os << "}";
return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
os << "{";
for (auto it = mp.begin(); it != mp.end();) {
os << it->first << ":" << it->second;
if (++it != mp.end()) os << ",";
}
os << "}";
return os;
}
void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
cin >> t;
in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
if (opt.has_value())
os << opt.value();
else
os << fallback;
os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
for (auto it = vec.begin(); it != vec.end();) {
if ((*it).has_value())
os << (*it).value();
else
os << fallback;
if (++it != vec.end()) os << " ";
}
os << "\n";
}
namespace IO {
template <class T, class... U>
T read(U&&... u) {
T t = T(forward<U>(u)...);
in(t);
return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v;
u -= offset, v -= offset;
g[u].push_back(v);
if (!directed) g[v].push_back(u);
}
return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
vector<vector<pair<int, T>>> g(n);
for (int i = 0; i < m; i++) {
int u, v;
T w;
cin >> u >> v >> w;
u -= offset, v -= offset;
g[u].push_back({v, w});
if (!directed) g[v].push_back({u, w});
}
return g;
}
} // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
p -= offset;
if (to_root) g[i].push_back(p);
if (to_leaf) g[p].push_back(i);
}
return g;
}
} // namespace Tree
} // namespace IO
#line 10 "template/template.hpp"
#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
cerr << '\n';
}
template <class T1, class T2, class... T3>
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 "number-theory/pollard-rho.hpp"
#line 2 "number-theory/miller-rabin.hpp"
namespace MillerRabin {
using u64 = uint64_t;
using u128 = __uint128_t;
namespace internal {
u64 multiply_mod(u64 a, u64 b, u64 mod) { return u128(a) * b % mod; }
u64 power_mod(u64 a, u64 n, u64 mod) {
u64 ret = 1;
while (n) {
if (n & 1) ret = multiply_mod(ret, a, mod);
a = multiply_mod(a, a, mod);
n >>= 1;
}
return ret;
}
}; // namespace internal
bool is_prime(long long n) {
if (n < 2) return false;
u64 x = n;
for (u64 p : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
if (x % p == 0) return x == p;
}
int s = __builtin_ctzll(x - 1);
u64 d = (x - 1) >> s;
for (u64 a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
if (a % x == 0) continue;
u64 y = internal::power_mod(a % x, d, x);
if (y == 1 || y == x - 1) continue;
bool composite = true;
for (int r = 1; r < s; r++) {
y = internal::multiply_mod(y, y, x);
if (y == x - 1) {
composite = false;
break;
}
}
if (composite) return false;
}
return true;
}
}; // namespace MillerRabin
/**
* @brief Miller-Rabin 素数判定
* @docs docs/number-theory/miller-rabin.md
*/
#line 4 "number-theory/pollard-rho.hpp"
namespace PollardRho {
using ll = long long;
using u64 = uint64_t;
namespace internal {
u64 random() {
static u64 x = 0x243f6a8885a308d3ULL;
x ^= x << 7;
x ^= x >> 9;
return x;
}
u64 find_factor(u64 n) {
if (n % 2 == 0) return 2;
if (n % 3 == 0) return 3;
while (true) {
u64 y = random() % (n - 1) + 1;
u64 c = random() % (n - 1) + 1;
u64 m = 128, g = 1, r = 1, q = 1, x = 0, z = 0;
auto f = [&](u64 v) {
return (MillerRabin::internal::multiply_mod(v, v, n) + c) % n;
};
while (g == 1) {
x = y;
for (u64 i = 0; i < r; i++) y = f(y);
for (u64 k = 0; k < r && g == 1; k += m) {
z = y;
for (u64 i = 0; i < min(m, r - k); i++) {
y = f(y);
u64 d = x > y ? x - y : y - x;
q = MillerRabin::internal::multiply_mod(q, d, n);
}
g = gcd(q, n);
}
r <<= 1;
}
if (g == n) {
do {
z = f(z);
u64 d = x > z ? x - z : z - x;
g = gcd(d, n);
} while (g == 1);
}
if (g != n) return g;
}
}
void factorize(u64 n, vector<u64>& factors) {
if (n == 1) return;
if (MillerRabin::is_prime(n)) {
factors.push_back(n);
return;
}
u64 d = find_factor(n);
factorize(d, factors);
factorize(n / d, factors);
}
}; // namespace internal
vector<pair<ll, int>> factorize(ll n) {
assert(n >= 1);
vector<u64> factors;
internal::factorize(n, factors);
sort(factors.begin(), factors.end());
vector<pair<ll, int>> ret;
for (u64 p : factors) {
if (ret.empty() || ret.back().first != (ll)p)
ret.emplace_back(p, 1);
else
ret.back().second++;
}
return ret;
}
vector<ll> divisors(ll n) {
vector<ll> ret{1};
for (auto [p, e] : factorize(n)) {
size_t size = ret.size();
ll q = 1;
while (e--) {
q *= p;
for (size_t i = 0; i < size; i++) ret.push_back(ret[i] * q);
}
}
sort(ret.begin(), ret.end());
return ret;
}
}; // namespace PollardRho
/**
* @brief Pollard's rho algorithm
* @docs docs/number-theory/pollard-rho.md
*/
#line 5 "verify/number-theory/LC_factorize.test.cpp"
int main() {
int Q;
in(Q);
while (Q--) {
long long n;
in(n);
vector<long long> factors;
for (auto [p, e] : PollardRho::factorize(n))
while (e--) factors.push_back(p);
cout << factors.size();
for (long long p : factors) cout << ' ' << p;
cout << '\n';
}
}
verify/number-theory/LC_factorize.test.cpp
template/debug.hpp