Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
const int INF = 1 << 29;
inline int two(int n) { return 1 << n; }
inline int test(int n, int b) { return (n >> b) & 1; }
inline void set_bit(int& n, int b) { n |= two(b); }
inline void unset_bit(int& n, int b) { n &= ~two(b); }
inline int last_bit(int n) { return n & (-n); }
inline int ones(int n) {
  int res = 0;
  while (n && ++res) n -= n & (-n);
  return res;
}
template <class T>
void chmax(T& a, const T& b) {
  a = max(a, b);
}
template <class T>
void chmin(T& a, const T& b) {
  a = min(a, b);
}
int main() {
  long long t;
  cin >> t;
  while (t--) {
    vector<long long> v;
    long long n;
    cin >> n;
    long long a = 2;
    int c = 0;
    while (n >= 1 && a <= sqrt(n)) {
      if (ceil(n / (a * 1.0)) == n / a) {
        n = n / a;
        v.push_back(a);
        c++;
      }
      if (c == 2) {
        break;
      }
      a++;
    }
    if (v.size() < 2) {
      cout << "NO" << endl;
    } else {
      if (v[0] != n && v[1] != n) {
        cout << "YES" << endl;
        cout << v[0] << " " << v[1] << " " << n << endl;
      } else {
        cout << "NO" << endl;
      }
    }
  }
  return 0;
}