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
t=int(input())
while t>0:
    d=list()
    n=int(input())
    imp=int(n)
    ctr=0
    for i in range (2,int(sqrt(n))):
        while(n%i==0):
            n//=i
            d.append(i)
            
    if(n>1):
        d.append(n)

    if(len(set(d))==2 and len(d)>=4):
        print("YES")
        print(d[0],d[-1],int(imp/(d[0]*d[-1])))
        ctr+=1
    
    if(len(set(d))>=3 or len(d)>=6 and ctr!=1 ):
            print("YES")
            if(len(set(d))>=3):
                print(d[0],d[-1],int(imp/(d[0]*d[-1])))
                ctr+=1
            else:
                print(d[0],d[0]**2,int(imp/(d[0]**3)))
                ctr+=1
    
    if(ctr==0):
        print("NO")
    t-=1