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:
fast=lambda:stdin.readline().strip()
zzz=lambda:[int(i) for i in fast().split()]
z,zz=input,lambda:list(map(int,z().split()))
szz,graph,mod,szzz=lambda:sorted(zz()),{},10**9+7,lambda:sorted(zzz())
from re import *
from sys import *
from math import *
from heapq import *
from queue import *
from bisect import *
from string import *
from itertools import *
from collections import *
from math import factorial as f
from bisect import bisect as bs
from bisect import bisect_left as bsl
from collections import Counter as cc
from itertools import accumulate as ac
def lcd(xnum1,xnum2):return (xnum1*xnum2//gcd(xnum1,xnum2))
def output(answer):stdout.write(str(answer))
###########################---Test-Case---#################################
"""

  If you Know me , Then you probably don't know me !


"""
###########################---START-CODING---##############################

num=int(z())

for _ in range( num ):
    n=int(fast())
    x=int(n**.5)
    lst=[]
    for i in range(2,x+1):
        if n%i==0:
            lst.append(i)
            n//=i
        if len(lst)==2:
            if lst[1]!=n and lst[0]!=n:
                lst.append(n)
                break

    if len(lst)==3:
        print('YES')
        print(*lst)
    else:
        print('NO')