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 collections import Counter


def min_del(n, mn):
    for x in range(max(2, mn), int(n ** .5) + 1):
        if n % x == 0:
            return x
    return n


for _ in range(int(input())):
    n = int(input())
    a = min_del(n, 1)
    ab = n // a
    b = min_del(ab, a + 1)
    c = n // b // a
    if c != a and c != b and c > 1:
        print("YES")
        print(a, b, c)
    else:
        print("NO")