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 *
t = int(input())
for z in range(t):
    n = int(input())
    na = True
    sq = ceil(sqrt(n)) + 1
    for a in range(2, sq):
        if not na:
            break
        if n % a == 0:
            q = n // a
            sq2 = ceil(sqrt(q)) + 1
            for b in range(a + 1, sq2):
                if q % b == 0:
                    if q // b > b:
                        print('YES')
                        print(a, b, q // b)
                        na = False
                        break

    if na:
        print('NO')

##a = n // (b * c)
##b * c = n // a = q
##b * c = q
##b = q // c