因为要保证 $a_{i} \vert a_{i+1}$,又要保证得到的数组最长,可以想到先把 $n$ 因数分解,得到个数最多的因子 $p$,能够保持整除关系并且最长的序列的长度就是 $p$ 的个数,其余的因子全部放在最后一个数字。
// Date: Mon Dec 11 20:15:03 2023
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
const int INF = 0x3f3f3f3f, MOD = 1e9 + 7;
const double eps = 1e-8;
const int dir[8][2] = {
{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1},
};
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef pair<int, int> PII;
const ull Pr = 131;
#define For(i, a, b) for (int i = int(a); i < int(b); ++i)
#define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i)
#define For1(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i)
#define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i])
#define f1 first
#define f2 second
#define pb push_back
#define has(a, x) (a.find(x) != a.end())
#define nonempty(a) (!a.empty())
#define all(a) (a).begin(), (a).end()
#define SZ(a) int((a).size())
#ifdef _DEBUG
#define debug1(x) cout << #x " = " << x << endl;
#define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl;
#define debug3(x, y, z) \
cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl;
#else
#define debug1
#define debug2
#define debug3
#endif
int t;
ll n;
map<ll, int> m;
void defact(ll n) {
for (ll i = 2; i * i <= n; i++) {
if (n % i == 0) {
while (n % i == 0) {
m[i]++;
n /= i;
}
}
}
if (n > 1)
m[n]++;
}
int main(void) {
#ifdef _DEBUG
freopen("1454d.in", "r", stdin);
#endif
std::ios::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin >> t;
while (t--) {
cin >> n;
m.clear();
defact(n);
ll ma = 0, val = 0;
for (auto &[x, y] : m) {
if (y > ma) {
ma = y;
val = x;
}
}
vector<ll> res(ma + 1, val);
cout << ma << '\n';
for (auto &[x, y] : m) {
int cnt = y;
if (x != val) {
while (cnt--) {
res[ma] *= x;
}
}
}
For1(i, 1, ma) { cout << res[i] << ' '; }
cout << '\n';
}
return 0;
}