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 PYTHON):

Solution:
t=int(input())
for i in range(t):
    n=int(input())

    def check(n):
        use=set()
        i=2
        while i*i<=n:
            if n%i==0 and i not in use:
                use.add(i)
                n/=i
                break
            i+=1
        i=2
        while i*i<=n:
            if n%i==0 and i not in use:
                use.add(i)
                n/=i
                break
            i+=1
        if n==1 or n in use or len(use)<2:
            return "NO"
        else:
            print "YES"
            use.add(n)
            for i in use:
                print i,
        return ""

    print check(n)