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 
from math import sqrt


def primes(n):
    y, count, result = n, 0, list()
    for i in range(2, int(sqrt(n)) + 1):
        if y % i == 0:
            count += 1
            y = y // i
            result.append(i)
            if count >= 2:
                break
    print("YES" if count >= 2 and y not in result else "NO")
    if count >= 2 and y not in result:
        print(*(result + [y]))


for _ in range(int(input())):
    primes(int(input()))
