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

def divide(n, start):
    for k in range(start, int(sqrt(n)) + 1):
        if n % k == 0:
            return k
    return n


for _ in range(int(input())):
    n = int(input())
    a = divide(n, 2)
    if a == n:
        print('NO')
        continue
    n //= a
    b = divide(n, a + 1)
    if b == n:
        print('NO')
        continue
    n //= b
    if n <= b:
        print('NO')
        continue
    print('YES')
    print(a, b, n)