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

for case in range (int (input ())) :
    n = int (input())
    a, b, c = 0, 0, 0

    for i in range(2, int (math.sqrt (n)) + 1) :
        if n % i == 0 :
            a, b = i, n // i
            break
    if a :
        for i in range (a + 1, int (math.sqrt(b)) + 1) :
            if b % i == 0 :
                b, c = i, b // i
                break
    
    print ("YES\n" + ' '.join ([str (a), str (b), str (c)]) if a >= 2 and b >= 2 and c >= 2 and b != c else "NO")