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:
for _ in range(int(input())):
    n=int(input())
    sq=int(n**0.5 +1)
    a=[]
    
    d={}
    
    for i in range(2,sq):
        if(n%i==0):
            x=n//i
            a.append(i)
            
            d[i]=x
            d[x]=i
    ch=1    

    for i in range(len(a)):
        for j in range(i+1,len(a)):
            try:
                x=d[ a[i]*a[j] ]
                y=a[i]
                z=a[j]
                if(x!=y)and(x!=z):
                    ch=2
                    
                    break
            except:
                continue
        if(ch==2):
            break
    if(ch==2):
        
        print("YES")
        print(x,y,z)
    else:
        print("NO")