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:
import math

def divisorGenerator(n):
    large_divisors = []
    for i in range(1, int(math.sqrt(n) + 1)):
        if n % i == 0:
            yield i
            if i*i != n:
                large_divisors.append(n / i)
    for divisor in reversed(large_divisors):
        yield divisor
        
def solver(k):
    divs = list(divisorGenerator(k))[1:-1]


    if len(divs) > 0:
        a = int(divs[0])
        second_divs =  [el for el in list(divisorGenerator(k//a))[1:-1] if el > a]
        if len(second_divs) > 0:
            b = int(second_divs[0])
            c = int(k // b // a)
            if k % (b * a) == 0 and c > b:
                print('yes')
                print(f'{a} {b} {c}')

            else:
                print('no')
        else:
            print('no')

    else:
        print('no')
        
n = int(input())
for i in range(n):

    k = int(input())
    solver(k)