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 sys import stdin, stdout

fin = lambda: stdin.readline()

fout = lambda *args: stdout.write(' '.join(str(i) for i in args) + '\n')


def f(n, s=2):
    a, b = -1, -1
    for i in range(s, 22361):
        if n % i == 0:
            if a == -1:
                a = i
                n //= i
            elif i < n // i:
                return a, i, n // i
    return -1


for _ in range(int(fin())):
    n = int(fin())
    a = f(n)
    if a == -1:
        fout('NO')
    else:
        fout('YES')
        fout(a[0], a[1], a[2])