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
import math
t=int(stdin.readline().rstrip())
while t>0:
    n=int(stdin.readline().rstrip())
    p=int(math.floor(math.sqrt(n)))
    l=[]
    a,b=-1,-1
    for i in range(2,p+1):
        if n%i==0:
            a=i
            n//=a
            break
    for i in range(2,p+1):
        if n%i==0 and i!=a:
            b=i
            n//=b
            break
    f=0
    if n==1 or n==a or n==b:
        f=1
    if a==-1 or b==-1:
        f=1
    if f==0:
        print("YES")
        print(str(a)+" "+str(b)+" "+str(n))
    else:
        print("NO")
    t-=1