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 solution(n):
    for first_dis in range(2, int(n**0.5) + 1):
        if n % first_dis == 0:
            next_value = n // first_dis
            for second_dis in range(first_dis + 1, int(next_value**0.5) + 1):
                if next_value % second_dis == 0:
                    third = next_value // second_dis
                    if third != second_dis:
                        return ("YES", f"{first_dis} {second_dis} {third}")
    return ("NO",)


def read():
    cnt = int(input())
    for _ in range(cnt):
        value = int(input())
        for item in solution(value):
            print(item)

read()