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  
  
# method to print the divisors 
def printDivisors(n) : 
      
    # Note that this loop runs till square root 
    i = 2
    l=[]
    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
def find3(A, arr_size, s):
    A.sort()
    p=0
    for i in range(0, arr_size-2):
        l = i + 1
        r = arr_size-1 
        while (l < r): 
            if( A[i] * A[l] * A[r] == s):
                print("YES")
                print(A[i],A[l],A[r])
                p=1
                break
            elif (A[i] * A[l] * A[r] < s): 
                l += 1
            else:
                r -= 1
        if p==1:
            break
    if p==0:
       print("NO")
t=int(input())
while t:
    t-=1 
    n=int(input())
    l=printDivisors(n)
    find3(l,len(l),n)