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 floor, sqrt, ceil

t = int(input())
for _ in range(t):
    a = -1
    b = -1
    n = int(input())
    i = 2
    while i*i < n:
        if n % i == 0:
            a = i
            n //= a
            break
        i += 1
    i = 2
    while i*i < n:
        if n % i == 0 and i != a:
            b = i
            n //= b
            break
        i += 1
    if a == -1 or b == -1 or n == 1 or n == a or n == b:
        print('NO')
        continue
    print('YES')
    print(a, b, n)