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:
def smallestDivisor(start,n): 
  
    # if divisible by 2 
    if (n % 2 == 0 and start == 2): 
        return 2; 
  
    # iterate from 3 to sqrt(n) 
    i = start;  
    while(i * i <= n): 
        if (n % i == 0): 
            return i; 
        i += 1; 
  
    return n; 
    
t = int(input())
for i in range(t):
    n = int(input())
    a = smallestDivisor(2, n)
    b = smallestDivisor(a+1, n/a)
    c = n//(a*b)
    if c!=1 and c!=a and c!=b:
        print('YES')
        print(a,b,c)
    else:
        print('NO')