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:
from math import sqrt
from math import ceil


def find(fro, n):
    if n % fro == 0:
        return fro
    return find(fro + 1, n)


t = int(input())
answers = []
for ti in range(t):
    n = int(input())

    first = -1
    for i in range(2, ceil(sqrt(n)) + 1):
        if n % i == 0:
            first = i
            break

    if first == -1:
        answers.append("NO")
        continue

    second = -1
    nn = n // first
    for i in range(first + 1, ceil(sqrt(nn))):
        if nn % i == 0:
            second = i
            break

    if second == -1:
        answers.append("NO")
        continue

    third = nn // second
    answers.append("YES")
    answers.append(str(first) + " " + str(second) + " " + str(third))


for a in answers:
    print(a)