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
def pd(n,not_include) : 
    li = []  
      
    for i in range(2, int(math.sqrt(n) + 1)) : 
          
        if (n % i == 0) : 
              
            if (n / i == i) :
                if n!=not_include:
                    lis=[]
                    lis.append(i)
                    lis.append(i)
                    #li.append(lis) 
            else : 
                lis=[]
                if i!=not_include and n//i!=not_include:
                    lis.append(i)
                    lis.append(n//i)
                    li.append(lis) 
    return li    
t=(int)(input())
for wirfb in range(t):
    n=(int)(input())
    li=pd(n,1)
    f=0
    if len(li)>=1:
        for x in li:
            lis=pd(x[1],x[0])
            if len(lis)>=1:
                f=1
                break;
            else:
                f=0
                
    else:
        f=0
    if f==0:
        print("NO")
    else:
        print("YES")
        print(x[0],lis[0][0],lis[0][1])