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:
def Divisors(number):
    Div=set()
    sqr=int(number**0.5)
    for i in range(2,sqr+1):
        if number%i==0:
          Div=Div|{i}
          Div=Div|{(number//i)}
    return list(Div)
def getDiv(Number):
        D=list(Divisors(Number))
        D.sort()
        for i in range(len(D)):
            for j in range(i+1,len(D)):
                m=D[i]*D[j]
                if m in D and  Number//m !=D[i] and Number//m !=D[j] :
                    r=str(D[i])+' '+str(D[j])+' '+str(Number//m)
                    r='YES\n'+r
                    return r
        return 'NO'

Answers=[]
n=int(input())
for i in range(n):
    a=int(input())
    Answers.append(getDiv(a))
for i in Answers:
    print(i)