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 collections import Counter
from collections import defaultdict
import math
  
# method to print the divisors 
def factors(n) : 
    l=list()  
    # Note that this loop runs till square root 
    i = 1
    while i <= math.sqrt(n): 
          
        if (n % i == 0) : 
              
            # If divisors are equal, print only one 
            if (n / i == i) : 
                l.append(i) 
            else : 
                # Otherwise print both 
                l.append(i)
                l.append(n//i) 
        i = i + 1
    return l
t=int(input())
for _ in range(0,t):
    n=int(input())
    l=factors(n)
    #print(l,t)
    if(len(l)==2):
        print("NO")
        continue
    else:
        a=l[2]
        b=n//a
        l2=factors(b)
        f=0
        #print(a,l2)
        if(len(l2)==2):
            print("NO")
            continue
        for i in range(2,len(l2)):
            if(a!=l2[i] and l2[i]!=b//l2[i] and b//l2[i]!=a and a>=2 and l2[i]>=2 and b//l2[i]>=2):
                f=1
                print("YES")
                print(a,l2[i],b//l2[i])
                break
        if(f==0):
            print("NO")