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 PYTHON3):

Solution:
import math


def deliteli_chisla(cur):
    mas = []
    ot = "NO"
    n = cur
    for i in range(2, math.ceil(cur ** 0.5)):
        if n % i == 0:
            mas.append(i)
    for i in range(len(mas)):
        del1 = mas[i]
        nn = n // del1
        s = nn
        for j in range(i, len(mas)):
            nn = s
            if nn % mas[j] == 0:
                nn = nn // mas[j]
                del2 = mas[j]
                if del1 * del2 != n and n % (del1 * del2) == 0:
                    if del1 != del2 and del2 != (n // del1 // del2) and del1 != n // del1 // del2:
                        ot = "YES\n" + str(del1) + " " + str(del2) + " " + str(n // del1 // del2)

                        return ot


for t in range(int(input())):
    n = int(input())
    if deliteli_chisla(n) is None:
        print("NO")
    else:
        print(deliteli_chisla(n))