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:
from functools import reduce

def factors(n):    
    return set(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
t = int(input())
#for each test cases
for i in range(t):
    n=int(input())
    def x(n):
        x=factors(n)
        counter=1
        if (len(x)<5):
            return True
        else:
            x=x-set([1])-set([n])
            x=list(x)
            for i in range(len(x)-2):
                for j in range (i+1,len(x)-1):
                    for k in range (j+1,len(x)):
                        if(x[i]*x[j]*x[k]==n):
                            print("YES")
                            print(x[i],x[j],x[k])
                            return False
        return True
    if x(n):
        print("NO")