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:
t=int(input())
while(t):
    l=set()
    tr=0
    
    n=int(input())
    ce=n
    if n>=12:
        i=2
        while(n>0 and tr<3 ):
            if tr<2 and i*i>ce:
                break
            if tr==2:
            
                l.add(int(n))
                tr=tr+1
                break
            elif n%i==0:
                
                l.add(i)
                tr=tr+1
                n=n/i
            elif tr==2:
                l.add(int(n))
                tr=tr+1
                break
            i=i+1    
    if tr==3  and len(l)==3:
       
        print("YES")
        l=list(l)
        l.sort()
        for i in range (3):
            print(l[i],end=" ")
        print()    
    else:
        print("NO")   
 
    t=t-1