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:
from math import sqrt
test = int(input())
while test > 0:
    test -= 1 
    n = int(input())
    first = []
    sz = 0
    for i in range (2, int(sqrt(n)+1)):
        if(n % i == 0):
            first.append(i)
            sz += 1
    
    found = False
    for i in range (sz):
        for j in range (i+1, sz):
            if first[i] != first[j] and n % (first[i]*first[j]) == 0\
            and n / (first[i]*first[j]) != first[i] and n / (first[i]*first[j]) != first[j]:
                print("YES")
                print(first[i], end = " ")
                print(first[j], end = " ")
                print(int(n / (first[i]*first[j])))
                found = True
                break
        if(found): break
    
    if(found == False): print("NO")