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:
# Product of three numbers

from math import *
for i in range(int(input())):
    num = int(input())
    if 2*3*4 > num:
        print("NO")
    else:
        a,b = 0,0
        for i in range(2, int(sqrt(num))+1):
            if num % i == 0:
                a = i
                num //= i
                break
        for i in range(2, int(sqrt(num))+1):
            if num % i == 0 and i != a:
                b = i
                num//= i
                break
        if a==0 or b==0 or num==b or num ==a:
            print("NO")
        else:
            print("YES")
            print(a,b,num)