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 sys
import math
from collections import Counter
from collections import OrderedDict
from collections import defaultdict
from functools import reduce
sys.setrecursionlimit(10**6)
def inputt():
    return sys.stdin.readline().strip()
def printt(n):
    sys.stdout.write(str(n)+'\n')
def listt():
    return [int(i) for i in inputt().split()]
 
def gcd(a,b): 
   return math.gcd(a,b) 
 
def lcm(a,b): 
    return (a*b) // gcd(a,b) 

def factors(n):
    step = 2 if n%2 else 1
    return set(reduce(list.__add__,([i, n//i] for i in range(1, int(math.sqrt(n))+1, step) if n % i == 0)))

def comb(n,k):
    factn=math.factorial(n)
    factk=math.factorial(k)
    fact=math.factorial(n-k)
    ans=factn//(factk*fact)
    return ans

def is_prime(n): 
    if n <= 1: 
        return False
    if n == 2: 
        return True
    if n > 2 and n % 2 == 0: 
        return False

    max_div = math.floor(math.sqrt(n)) 
    for i in range(3, 1 + max_div, 2): 
        if n % i == 0: 
            return False
    return True
def maxpower(n,x):
    B_max = int(math.log(n, x)) + 1#tells upto what power of x n is less than it like 1024->5^4
    return B_max

def sf(s,n):
    for i in range(s,int(math.sqrt(n)+1)):
        if n%i==0:
            n=n//i
            return i,n
    return 1,n    

        
t=int(inputt())
#t=1

for _ in range(t):
    a,b,c=1,1,1
    n=int(inputt())
    a,n=sf(2,n)
    b,n=sf(a+1,n)
    c=n
    #print(a,b,c)                
    if a!=b and b!=c and c!=1 and a!=c and a!=1 and b!=1:
        print("YES")
        print(a,b,c)
    else:
        print("NO")