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 solve(n):
    a, b, c = None, None, None
    for i in range(2, int(n**0.5) + 1):
        if n%i == 0:
            a = i
            n = n/i
            break
    else:
        return None
    for i in range(a+1, int(n**0.5) + 1):
        if n%i == 0:
            b = i
            c = int(n/i)
            break
    else:
        return None

    if b != c and a != c:
        return (a, b, c)
    else:
        return None    

t = int(input())

for _ in range(t):
    n = int(input())
    
    res = solve(n)
    
    if res:
        print('YES')
        print (*res)
    else:
        print ('NO')