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())
    n2=n
    prime={}
    z=int((n**(1/2)))
    i=2 
    while(i<z+1):
        if n%i==0:
            prime[i]=prime.get(i,0)+1 
            n=n//i   
            z=int((n**(1/2)))
            i=2
            continue
        else:
            i+=1
    else:
       
        prime[int(n)]=prime.get(int(n),0)+1 
    n=n2
    if len(prime)>=2:
        output=[]
        c=0
        for i in prime:
            if c>=2:
                break
            output.append(i)
            c+=1 
        product=output[0]*output[1] 
        
        if n//product!=1 and n//product not in output:
            print("YES")
            print(output[0],output[1],n//product)
        else:
            print("NO")
            
        
    if len(prime)==1:
        for i in prime:
            if prime[i]>=6:
                print("YES")
                print(i,i**i,i**(prime[i]-3))
            else:
                print("NO")