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:
#!/usr/bin/env python
# coding: utf-8

# In[7]:


import math
def divisor(n):
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            k=n//i
            for j in range(2,int(math.sqrt(k))+1):
                if j!=i and k%j==0:
                    t=k//j
                    if t!=i and t!=j:
                        return ["YES",i,j,t]
    return "NO"
t=int(input())
for i in range(t):
    n=int(input())
    if divisor(n)=="NO":
        print("NO")
    else:
        print(divisor(n)[0])
        print(*divisor(n)[1:])


# In[ ]: