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 sys
import math
input=sys.stdin.readline

 
  
# A function to print all prime factors of  
# a given number n 
def primeFactors(n): 
      
    # Print the number of two's that divide n 
    while n % 2 == 0: 
         
        n = n / 2
        return(2,n)
          
    # 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: 
             
            n = n / i 
            return(i,n)
              
    # Condition if n is a prime 
    # number greater than 2 
    return(-1,-1)
    
t=int(input())
for _ in range(t):
    n=int(input())
    a,n=primeFactors(n)
    b=-1
    c=-1
    flag=0
    if(a==-1):
        print("NO")
    else:
        i=2
        while(i<=math.sqrt(n)):
            if(n%i==0):
                if(n//i>=2):
                    if(i!=a and(n//i!=a and i!=n//i)):
                        b=i
                        c=n//i
                        flag=1
            i+=1
        if(flag==1):
            print("YES")
            print(a,int(b),int(c))
        else:
            print("NO")