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:

# Python program to print prime factors 
  
import math 
  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
    a=[]  
    # Print the number of two's that divide n 
    while n % 2 == 0: 
        a.append(2), 
        n = n // 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            a.append(i) 
            n = n // i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        a.append(n) 
    return a
# Driver Program to test above function 

  
# This code is contributed by Harshit Agrawal 

def prod(a):
    s=1
    for i in range(len(a)):
        s=s*a[i]
    return s

t=int(input())
for i in range(t):
    n=int(input())
    b=primeFactors(n)
    c=list(set(b))
    if len(c)>=3:
        print("YES")
        print(c[0],c[1],n//(c[0]*c[1]))
    elif len(c)==2 and len(b)>=4:
        print("YES")
        print(c[0],c[1],n//(c[0]*c[1]))
    elif len(c)==1 and len(b)>=6:
        print("YES")
        print(c[0],c[0]**2,n//(c[0]**3))
    else:
        print("NO")