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:
import  math
b= int(input())
t=[]
for j in range(b):
    t.append(int(input()))
for a in t :
    c=3
    i = 2
    s = ''
    while a > 1 and a // i >= 1 and i <=math.pow(a,1/c):
        if (a % i == 0):
            a = a // i
            s = s + i.__str__() + ' '
            c=c-1
            if (s.split(' ').__len__()>2  and a//(i+1)>0):
                s = s + a.__str__() + ' '
                a=0
            elif s.split(' ').__len__()>2:
                a=0
        i = i + 1

    if s.split(' ').__len__()>3:
        print("YES \n", s, sep='')
    else:
        print("NO")