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:
t=int(input())
from math import sqrt
primes=[True for i in range(10**5)]
for i in range(2,len(primes)):
    jumper=i
    ind=2
    while i*ind<len(primes):
        primes[i*ind]=False
        ind+=1
primes=set([i for i in range(len(primes)) if primes[i]])

def divider(x):
    if x%2==0:
        return x//2,2
    for i in range(3,int(sqrt(x)+1),2):
        #print("Inside loop:",i)
        if x%i==0:
            return x//i,i
    return -1,-1
    
for _ in range(t):
    n=int(input())
    flag=False
    ans1,ans2,ans3=0,0,0
    for i in range(2,int(sqrt(n)+1)):
        #print(i)
        reali=n//i
        if n%i==0 and n//i not in primes:
            ans2,ans3=divider(n//i)
            if ans2==-1 and ans3==-1:
                continue
            ans1=i
            if ans1!=ans2 and ans2!=ans3 and ans3!=ans1:
                flag=True
                break
    if flag:
        print("YES")
        print(ans1,ans2,ans3)
    else:
        print("NO")