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
n=int(input())
for i in range(n):
    m=int(input())
    m1=m
    c=2
    p=[]
    while len(p)<3 and c<=sqrt(m1):
        if m%c==0:
            m=m//c
            p.append(c)
        else:
            c=c+1
    if len(p)==3:        
        if p[0]==p[1]:
            p[1]=p[1]*p[2]
        p[2]=m1//p[0]//p[1]
    if len(p)==2:
        p.append(m1//p[0]//p[1])    
    if len(p)==3 and p[2]>1 and p[0]!=p[2] and p[1]!=p[2] and p[0]!=p[1]:
            print ('YES')
            print (*p)
    else:   
        print ('NO')