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:
"""
1294C
"""

def inp():
    """
    For taking integer inputs.
    """
    return(int(input()))

def get_n_ints(n):
    """
    For taking List inputs.
    """
    result = []
    i = 0
    while i < n:
        val = input().rstrip("\n")
        result.append(int(val))
        i += 1
    return result

def problem(number):
    seen = list()
    i = 2
    while i*i <= number:
        if i not in seen:
            if number%i == 0:
                seen.append(i)
                number = number//i

        if len(seen) == 2 and number > seen[-1]:
            seen.append(number)
            print("YES")
            print(*(seen))
            return
        i += 1

    print("NO")




n = inp()
arr = get_n_ints(n)
for i in range(n):
    problem(arr[i])