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:
test_cases = int(input())
for z in range(test_cases):
    n = int(input())
    x=n
    l =[]
    for i in range(2,int(n**0.5)+2):
        if x%i==0:

            l.append(i)
            x=x/i

            if len(l)>=3 :
                if l[0]*l[1]*l[2]<=n:
                    print('YES')
                    print(l[0],l[1],int(n/(l[0]*l[1])))
                    break
            elif len(l)==2 and (l[0]*l[1])<=(n**0.5):
                print('YES')
                print(l[0], l[1], int(n / (l[0] * l[1])))
                break


    if len(l)<2:
        print('NO')

    if len(l)==2:
        if (l[0]*l[1])>(n**0.5) :
            print('NO')
    elif len(l)>=3:
        if l[0]*l[1]*l[2]>n:
            print('NO')