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
for _ in range(int(input())):
    n = int(input())
    t = n
    a1 = []
      
    
    while n % 2 == 0: 
        a1.append(2), 
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            a1.append(int(i)), 
            n = n / i          
    if n > 2: 
        a1.append(int(n))

    l = len(a1)
    a = list(set(a1))
    p = len(a)
    if p == 1 and l >= 6:
        if a[0] != t//(a[0]**3) and a[0]**2 != t//(a[0]**3):
            print("YES")
            print(a[0],a[0]**2,t//(a[0]**3))
        else:
            print("NO")
              
    elif (p >= 2 )and (l>= 3):
        if a[0] != t//(a[0]*a[1]) and a[1] != t//(a[0]*a[1]):
            
            print("YES")
            print(a[0],a[1],t//(a[0]*a[1]))
        else:
            print("NO")
    else:
        print("NO")