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 ceil, sqrt

T = int(input())
answer = ""

for t in range(T):
    
    n = int(input())
    end = False

    add = []
    lim = ceil(sqrt(n)) + 1
    for a in range(2, lim):
        if n % a == 0:
            for b in range(a+1, lim):
                c = n / a / b
                if int(c) == c and c != b and c != a and c != 1:
                    answer += "YES\n"
                    c = int(n / a / b)
                    answer += "{} {} {}\n".format(a, b, c)
                    end = True
                    break
        if end:
            break

    if not end:
        answer += "NO\n"

print(answer)