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:
import math
t = int(input())
while t>0:
    # print("t: ",t)
    t-=1
    n = int(input())
    num_factors=0
    first_factor = -1
    second_factor = -1

    if n==1 or n==2:
        print("NO")
        continue

    n_copy=n
    s = int(math.sqrt(n))
    for i in range(2,s):
        if n_copy%i==0:
            if first_factor==-1:
                first_factor=i
            elif second_factor==-1:
                second_factor=i
            else:
                break
            n_copy= n_copy//i
    if first_factor==-1 or second_factor==-1 or first_factor==n_copy or second_factor==n_copy or n_copy==1:
        print("NO")
    else:
        print("YES")
        print(first_factor,second_factor,n_copy)