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 sys import stdin


def f(n):
    res=[]
    for i in range(2,int(n**0.5)+1):
        if n%i==0 and i not in res:
            n=n//i
            res.append(i)
            break
    for i in range(2,int(n**0.5)+1):
        if n%i==0 and i not in res:
            n=n//i
            res.append(i)
            break
    if len(res) < 2 or n in res or n == 1:
        return False
    else:
        return res+[n]
t=int(stdin.readline().strip())
for _ in range(t):
    n=int(stdin.readline().strip())
    res=f(n)
    if res==False:
        print('NO')
    else:
        print('YES')
        print(' '.join(map(str,res)))